Class 10 – Banking & Compound Interest

$\displaystyle \textbf{Question 1. }\text{Given the following details, calculate simple interest at the rate of }6\%\text{ per annum}$
$\displaystyle \text{up to June 30.} \hspace{0.2cm}\text{[ICSE 2003]}$

$\displaystyle \begin{array}{|l|c|c|c|} \hline \text{Date} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)} \\ \hline \text{Jan 1} & - & 24000 & 24000 \\ \hline \text{Jan 20} & 5000 & - & 19000 \\ \hline \text{Jan 29} & - & 10000 & 29000 \\ \hline \text{March 15} & - & 8000 & 37000 \\ \hline \text{April 3} & - & 7653 & 44653 \\ \hline \text{May 6} & 3040 & - & 41613 \\ \hline \text{May 8} & - & 5087 & 46700 \\ \hline \end{array}$

$\displaystyle \text{Answer:}$
$\displaystyle \text{Qualifying principal for various months:}$

$\displaystyle \begin{array}{|l|c|} \hline \text{Month} & \text{Principal (Rs.)} \\ \hline \text{January} & 19000 \\ \hline \text{February} & 29000 \\ \hline \text{March} & 29000 \\ \hline \text{April} & 44653 \\ \hline \text{May} & 46700 \\ \hline \text{June} & 46700 \\ \hline \text{Total} & 215060 \\ \hline \end{array}$

$\displaystyle P=\text{Rs. }215060$
$\displaystyle R=6\%\text{ and }T=\frac{1}{12}\times6=\frac{1}{2}$
$\displaystyle I=P\times R\times T$
$\displaystyle =215060\times\frac{6}{100}\times\frac{1}{2}$
$\displaystyle =\text{Rs. }1075.30$

$\\$

$\displaystyle \textbf{Question 2. }\text{Mr. Ashok has an account in the Central Bank of India. The following entries are from his passbook:-}$

$\displaystyle \text{If Mr. Ashok gets Rs. }83.75\text{ as interest at the end of the year, where the interest rate is}$
$\displaystyle \text{computed annually, calculate the rate of interest paid by the bank in his Savings Bank Account on }31\text{st}$
$\displaystyle \text{December }2005. \hspace{0.2cm}\text{[ICSE 2006]}$

$\displaystyle \text{Answer:}$
$\displaystyle \text{Qualifying principal for various months:}$

$\displaystyle \begin{array}{|l|c|} \hline \text{Month} & \text{Principal (Rs.)} \\ \hline \text{January} & 1300 \\ \hline \text{February} & 1600 \\ \hline \text{March} & 1600 \\ \hline \text{April} & 1600 \\ \hline \text{May} & 1600 \\ \hline \text{June} & 1600 \\ \hline \text{July} & 1600 \\ \hline \text{August} & 1600 \\ \hline \text{September} & 1600 \\ \hline \text{October} & 2300 \\ \hline \text{November} & 1700 \\ \hline \text{December} & 2000 \\ \hline \text{Total} & 20100 \\ \hline \end{array}$

$\displaystyle P=\text{Rs. }20100$
$\displaystyle \text{Rate}=r\%\text{ and }T=\frac{1}{12},\text{ Interest}=\text{Rs. }83.75$
$\displaystyle I=P\times R\times T$
$\displaystyle 83.75=20100\times\frac{r}{100}\times\frac{1}{12}$
$\displaystyle \Rightarrow r=5\%$

$\\$

$\displaystyle \textbf{Question 3. }\text{Kiran deposited Rs. }200\text{ per month for }36\text{ months in a bank's recurring deposit}$
$\displaystyle \text{account. If the bank pays interest at the rate of }11\%\text{ per annum, find the amount she gets on}$
$\displaystyle \text{maturity.} \hspace{0.2cm}\text{[ICSE 2012]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=\text{Rs. }200,\text{ no of months}=36,\text{ }r=11\%$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle =200\times36+200\times\frac{36(36+1)}{2\times12}\times\frac{11}{100}$
$\displaystyle =\text{Rs. }8421$
$\\$

$\displaystyle \textbf{Question 4. }\text{Mohan deposited Rs. }80\text{ per month in a cumulative deposit account for }6\text{ years.}$
$\displaystyle \text{Find the amount payable to him on maturity, it the rate of interest is }6\%\text{ per annum.}$
$\displaystyle \hspace{0.2cm}\text{[ICSE 2006]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=\text{Rs. }80,\text{ no of months}=72,\text{ }r=6\%$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle =80\times72+80\times\frac{72(72+1)}{2\times12}\times\frac{6}{100}$
$\displaystyle =\text{Rs. }6811.20$
$\\$

$\displaystyle \textbf{Question 5. }\text{Mr. R. K. Nair gets Rs. }6455\text{ at the end of one year at the rate of }14\%$
$\displaystyle \text{per annum in a recurring deposit account. Find the monthly installment.} \hspace{0.2cm}\text{[ICSE 2005]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=\text{Rs. }x,\text{ no of months}=12,\text{ rate}=14\%,\text{ Maturity Amount}=\text{Rs. }6455$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 6455=x\times12+x\times\frac{12(12+1)}{2\times12}\times\frac{14}{100}$
$\displaystyle x=\frac{6455}{12.91}=\text{Rs. }500$
$\displaystyle \text{He must deposit Rs. }500\text{ every month.}$
$\\$

$\displaystyle \textbf{Question 6. }\text{Ahmed has a recurring deposit account in a bank He deposits Rs. }2500\text{ per month}$
$\displaystyle \text{for }2\text{ years. If he gets Rs. }66250\text{ at the time of maturity, find: i) interest paid by the bank}$
$\displaystyle \text{ii) rate of interest.} \hspace{0.2cm}\text{[ICSE 2011]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=\text{Rs. }2500,\text{ no of months}=24,\text{ rate}=r\%,\text{ Maturity Amount}=\text{Rs. }66250$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 66250=2500\times24+2500\times\frac{24(24+1)}{2\times12}\times\frac{r}{100}\Rightarrow r=10\%$
$\displaystyle \text{Interest}=P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle =2500\times\frac{24(24+1)}{2\times12}\times\frac{10}{100}=6250$
$\\$

$\displaystyle \textbf{Question 7. }\text{The entries in a Saving Bank passbook are given below:}$

$\displaystyle \text{Calculate the interest for six months (January to June) at }4\%\text{ per Annum on the minimum balance}$
$\displaystyle \text{on or after the tenth day of each month.} \hspace{0.2cm}\text{[ICSE 2004]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Qualifying principal for various months:}$

$\displaystyle \begin{array}{|l|c|} \hline \text{Month} & \text{Principal (Rs.)} \\ \hline \text{January} & 14000 \\ \hline \text{February} & 20500 \\ \hline \text{March} & 20500 \\ \hline \text{April} & 20000 \\ \hline \text{May} & 21500 \\ \hline \text{June} & 23000 \\ \hline \end{array}$

$\displaystyle \text{Total}=\text{Rs. }119500$
$\displaystyle P=\text{Rs. }119500,\text{ }R=4\%\text{ and }T=\frac{1}{12}$
$\displaystyle I=P\times R\times T=119500\times\frac{4}{100}\times\frac{1}{12}$
$\displaystyle =\text{Rs. }398.33$
$\\$

$\displaystyle \textbf{Question 8. }\text{A page from the passbook of Mrs. Rama Bhalla is given below:}$

$\displaystyle \begin{array}{|l|l|c|c|c|} \hline \text{Date Year 2004} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)} \\ \hline \text{January 1} & \text{B/F} & - & - & 2000.00 \\ \hline \text{January 9} & \text{By Cash} & - & 200.00 & 2200.00 \\ \hline \text{February 10} & \text{To Cheque} & 500.00 & - & 1700.00 \\ \hline \text{February 24} & \text{By Cheque} & - & 300.00 & 2000.00 \\ \hline \text{July 29} & \text{To Cheque} & 200.00 & - & 1800.00 \\ \hline \text{November 7} & \text{By Cash} & - & 300.00 & 2100.00 \\ \hline \text{December 8} & \text{By Cash} & - & 200.00 & 2300.00 \\ \hline \end{array}$

$\displaystyle \text{Calculate the interest to Mrs. Rama Bhalla for the period of January }2004\text{ to December }2004,$
$\displaystyle \text{at the rate of }5\%\text{ per annum.} \hspace{0.2cm}\text{[ICSE 2005]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Qualifying principal for various months:}$

$\displaystyle \begin{array}{|l|c|} \hline \text{Month} & \text{Principal (Rs.)} \\ \hline \text{January} & 2200 \\ \hline \text{February} & 1700 \\ \hline \text{March} & 2000 \\ \hline \text{April} & 2000 \\ \hline \text{May} & 2000 \\ \hline \text{June} & 2000 \\ \hline \text{July} & 1800 \\ \hline \text{August} & 1800 \\ \hline \text{September} & 1800 \\ \hline \text{October} & 1800 \\ \hline \text{November} & 2100 \\ \hline \text{December} & 2300 \\ \hline \text{Total} & 23500 \\ \hline \end{array}$

$\displaystyle P=\text{Rs. }23500,\text{ }R=5\%\text{ and }T=\frac{1}{12}$
$\displaystyle I=P\times R\times T=23500\times\frac{5}{100}\times\frac{1}{12}$
$\displaystyle =\text{Rs. }97.92$
$\\$

$\displaystyle \textbf{Question 9. }\text{A page from Saving Bank account of Mr. Prateek is given below:}$

$\displaystyle \begin{array}{|l|l|c|c|c|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)} \\ \hline \text{January 1st 2006} & \text{B/F} & - & - & 1270 \\ \hline \text{January 7th 2006} & \text{By Cheque} & - & 2310 & 3580 \\ \hline \text{March 9th 2006} & \text{To Self} & 2000 & - & 1580 \\ \hline \text{March 26th 2006} & \text{By Cash} & - & 6200 & 7780 \\ \hline \text{June 10th 2006} & \text{To Cheque} & 4500 & - & 3280 \\ \hline \text{July 15th 2006} & \text{By Clearing} & - & 2630 & 5910 \\ \hline \text{October 18th 2006} & \text{To Cheque} & 530 & - & 5380 \\ \hline \text{October 27th 2006} & \text{To Self} & 2690 & - & 2690 \\ \hline \text{November 3rd 2006} & \text{By Cash} & - & 1500 & 4190 \\ \hline \text{December 6th 2006} & \text{To Cheque} & 950 & - & 3240 \\ \hline \text{December 23rd 2006} & \text{By Transfer} & - & 2920 & 6160 \\ \hline \end{array}$

$\displaystyle \text{If he receives Rs. }198\text{ as interest on }1\text{st January }2007.\text{ Find the rate of interest paid by the bank.}$
$\displaystyle \hspace{0.2cm}\text{[ICSE 2012]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Qualifying principal for various months:}$

$\displaystyle \begin{array}{|l|c|} \hline \text{Month} & \text{Principal (Rs.)} \\ \hline \text{January} & 3580 \\ \hline \text{February} & 3580 \\ \hline \text{March} & 1580 \\ \hline \text{April} & 7780 \\ \hline \text{May} & 7780 \\ \hline \text{June} & 3280 \\ \hline \text{July} & 3280 \\ \hline \text{August} & 5910 \\ \hline \text{September} & 5910 \\ \hline \text{October} & 2690 \\ \hline \text{November} & 4190 \\ \hline \text{December} & 3240 \\ \hline \text{Total} & 52800 \\ \hline \end{array}$

$\displaystyle P=\text{Rs. }52800,\text{ }R=x\%\text{ and }T=\frac{1}{12},\text{ }I=\text{Rs. }198$
$\displaystyle I=P\times R\times T$
$\displaystyle \Rightarrow 52800\times\frac{x}{100}\times\frac{1}{12}=198$
$\displaystyle \Rightarrow x=4.5\%$
$\\$

$\displaystyle \textbf{Question 10. }\text{Mrs. Kapoor opened a Saving Bank Account in State Bank of India on }9\text{th January }2008.$
$\displaystyle \text{Her passbook entries for the year }2008\text{ are given below:}$

$\displaystyle \begin{array}{|l|l|c|c|c|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)} \\ \hline \text{Jan. 9, 2008} & \text{By Cash} & - & 10000 & 10000 \\ \hline \text{Feb. 12, 2008} & \text{By Cash} & - & 15500 & 25500 \\ \hline \text{April 6, 2008} & \text{To Cheque} & 3500 & - & 22000 \\ \hline \text{April 30, 2008} & \text{To Self} & 2000 & - & 20000 \\ \hline \text{July 16, 2008} & \text{By Cheque} & - & 6500 & 26500 \\ \hline \text{Aug. 4, 2008} & \text{To Self} & 5500 & - & 21000 \\ \hline \text{Aug. 20, 2008} & \text{To Cheque} & 1200 & - & 19800 \\ \hline \text{Dec. 12, 2008} & \text{By Cash} & - & 1700 & 21500 \\ \hline \end{array}$

$\displaystyle \text{Mrs. Kapoor closed the account on }31\text{st December }2008.\text{ If the bank pays interest at }4\%\text{ per annum,}$
$\displaystyle \text{find the interest he receives on closing the account. Give your answer correct to the nearest rupee.}$
$\displaystyle \hspace{0.2cm}\text{[ICSE 2010]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Qualifying principal for various months:}$

$\displaystyle \begin{array}{|l|c|} \hline \text{Month} & \text{Principal (Rs.)} \\ \hline \text{January} & 10000 \\ \hline \text{February} & 10000 \\ \hline \text{March} & 25500 \\ \hline \text{April} & 20000 \\ \hline \text{May} & 20000 \\ \hline \text{June} & 20000 \\ \hline \text{July} & 20000 \\ \hline \text{August} & 19800 \\ \hline \text{September} & 19800 \\ \hline \text{October} & 19800 \\ \hline \text{November} & 19800 \\ \hline \text{Total} & 204700 \\ \hline \end{array}$

$\displaystyle P=\text{Rs. }204700,\text{ }R=4.0\%\text{ and }T=\frac{1}{12}$
$\displaystyle I=P\times R\times T=204700\times\frac{4}{100}\times\frac{1}{12}$
$\displaystyle =\text{Rs. }682.33\text{ or Rs. }682$
$\\$

$\displaystyle \textbf{Question 11. }\text{Explain the following:}$
$\displaystyle \text{i) Punnet has a recurring deposit account in Bank of Baroda and deposits Rs. }140\text{ per month for }4\text{ years.}$
$\displaystyle \text{If he gets Rs. }8092\text{ on maturity, find the rate of interest given by the bank.}$
$\displaystyle \text{ii) David opened a recurring deposit account in a bank and deposited Rs. }300\text{ per month for two years.}$
$\displaystyle \text{If he received Rs. }7725\text{ at the time of maturity, find the rate of interest per annum.} \hspace{0.2cm}\text{[ICSE 2008]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{i)}$
$\displaystyle P=\text{Rs. }140,\text{ no of months}=48,\text{ rate}=r\%,\text{ Maturity Amount}=\text{Rs. }8092$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 8092=140\times48+140\times\frac{48(48+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle r=\frac{(8092-140\times48)\times(2\times12)\times100}{140\times48\times49}\Rightarrow r=10\%$
$\displaystyle \text{ii)}$
$\displaystyle P=\text{Rs. }300,\text{ no of months}=24,\text{ rate}=r\%,\text{ Maturity Amount}=\text{Rs. }7725$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 7725=300\times24+300\times\frac{24(24+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle r=\frac{(7725-300\times24)\times(2\times12)\times100}{300\times24\times25}\Rightarrow r=7\%$
$\\$

$\displaystyle \textbf{Question 12. }\text{Amit deposited }150\text{ per month in a bank for }8\text{ month under the recurring deposit scheme.}$
$\displaystyle \text{What will be the maturity value of his deposits, if the rate of interest is }8\%\text{ per annum and interest}$
$\displaystyle \text{is calculated at the end of every month?} \hspace{0.2cm}\text{[ICSE 2001, 2007]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=\text{Rs. }150,\text{ no of months}=8,\text{ }r=8\%$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle =150\times8+150\times\frac{8(8+1)}{2\times12}\times\frac{8}{100}=\text{Rs. }1236$
$\\$

$\displaystyle \textbf{Question 13. }\text{Mr. Gupta opened a recurring deposit account in a bank. He deposited Rs. }2500\text{ per month}$
$\displaystyle \text{for two years. At the time of maturity, he got Rs. }67500.\text{ Find:}$
$\displaystyle \text{The total interest earned by Mr. Gupta}$
$\displaystyle \text{The rate of interest per annum.} \hspace{0.2cm}\text{[ICSE 2010]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=\text{Rs. }2500,\text{ no of months}=24,\text{ rate}=r\%,\text{ Maturity Amount}=\text{Rs. }67500$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 67500=2500\times24+2500\times\frac{24(24+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle r=\frac{(67500-2500\times24)\times(2\times12)\times100}{2500\times24\times25}\Rightarrow r=12\%$
$\displaystyle \text{Interest}=2500\times\frac{24(24+1)}{2\times12}\times\frac{12}{100}=\text{Rs. }7500$
$\\$

$\displaystyle \textbf{Question 14. }\text{Given below are the entries in a saving Bank A/C passbook:}$

$\displaystyle \begin{array}{|l|l|c|c|c|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)} \\ \hline \text{Feb. 8} & \text{B/F} & - & - & 8500 \\ \hline \text{Feb. 18} & \text{To Self} & 4000 & - & 4500 \\ \hline \text{April 12} & \text{By Cash} & - & 2230 & 6730 \\ \hline \text{June 15} & \text{To Self} & 5000 & - & 1730 \\ \hline \text{July 8} & \text{By Cash} & - & 6000 & 7730 \\ \hline \end{array}$

$\displaystyle \text{Calculate the interest for six months from February to July at }6\%\text{ p.a.} \hspace{0.2cm}\text{[ICSE 2013]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Qualifying principal for various months:}$

$\displaystyle \begin{array}{|l|c|} \hline \text{Month} & \text{Principal (Rs.)} \\ \hline \text{February} & 4500 \\ \hline \text{March} & 4500 \\ \hline \text{April} & 4500 \\ \hline \text{May} & 6730 \\ \hline \text{June} & 1730 \\ \hline \text{July} & 7730 \\ \hline \text{Total} & 29690 \\ \hline \end{array}$

$\displaystyle P=\text{Rs. }29690,\text{ }R=6\%\text{ and }T=\frac{1}{12}$
$\displaystyle I=P\times R\times T=29690\times\frac{6}{100}\times\frac{1}{12}$
$\displaystyle =\text{Rs. }148.45$
$\\$

$\displaystyle \textbf{Question 15. }\text{Chaudhary opened a saving bank account at State Bank of India on }1\text{st April }2007.$
$\displaystyle \text{The entries of one year as shown in his passbook are given below:}$

$\displaystyle \begin{array}{|l|l|c|c|c|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)} \\ \hline \text{1st April 2007} & \text{By Cash} & - & 8550.00 & 8550.00 \\ \hline \text{12th April 2007} & \text{To Self} & 1200.00 & - & 7350.00 \\ \hline \text{24th April 2007} & \text{By Cash} & - & 4550.00 & 11900.00 \\ \hline \text{8th July 2007} & \text{By Cheque} & - & 1500.00 & 13400.00 \\ \hline \text{10th Sept. 2007} & \text{By Cheque} & - & 3500.00 & 16900.00 \\ \hline \text{17th Sept. 2007} & \text{To Cheque} & 2500.00 & - & 14400.00 \\ \hline \text{11th Oct. 2007} & \text{By Cash} & - & 800.00 & 15200.00 \\ \hline \text{6th Jan. 2008} & \text{To Self} & 2000.00 & - & 13200.00 \\ \hline \text{9th March 2008} & \text{By Cheque} & - & 950.00 & 14150.00 \\ \hline \end{array}$

$\displaystyle \text{If the bank pays interest at the rate of }5\%\text{ per annum, find the interest paid on }1\text{st April }2008.$
$\displaystyle \text{Give your answer correct to nearest rupee.} \hspace{0.2cm}\text{[ICSE 2011]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Qualifying principal for various months:}$

$\displaystyle \begin{array}{|l|c|} \hline \text{Month} & \text{Principal (Rs.)} \\ \hline \text{April} & 7350 \\ \hline \text{May} & 11900 \\ \hline \text{June} & 11900 \\ \hline \text{July} & 13400 \\ \hline \text{August} & 13400 \\ \hline \text{September} & 14400 \\ \hline \text{October} & 14400 \\ \hline \text{November} & 15200 \\ \hline \text{December} & 15200 \\ \hline \text{January} & 13200 \\ \hline \text{February} & 13200 \\ \hline \text{March} & 14150 \\ \hline \text{Total} & 157700 \\ \hline \end{array}$

$\displaystyle P=\text{Rs. }157700,\text{ }R=5\%\text{ and }T=\frac{1}{12}$
$\displaystyle I=P\times R\times T=157700\times\frac{5}{100}\times\frac{1}{12}$
$\displaystyle =\text{Rs. }657.08\text{ or Rs. }657$
$\\$

$\displaystyle \textbf{Question 16. }\text{Bitto deposits a certain sum of money in a recurring deposit account of a Bank.}$
$\displaystyle \text{If the rate of interest of }8\%\text{ per annum and Mr. Bitto gets Rs. }8008\text{ from the bank}$
$\displaystyle \text{after }3\text{ years, find the value of his monthly installment.} \hspace{0.2cm}\text{[ICSE 2013]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=\text{Rs. }x,\text{ no of months}=36,\text{ rate}=8\%,\text{ Maturity Amount}=\text{Rs. }8008$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 8008=x\times36+x\times\frac{36(36+1)}{2\times12}\times\frac{8}{100}$
$\displaystyle x=\frac{8008}{40.44}=\text{Rs. }198.02$
$\displaystyle \text{He must deposit Rs. }200\text{ every month.}$
$\\$

$\displaystyle \textbf{Question 17. }\text{Shahrukh opened a recurring deposit account in a bank and deposited }800\text{ per month}$
$\displaystyle \text{for }1\frac{1}{2}\text{ years. If he received Rs. }15084\text{ at the time of maturity. Find the interest rate per annum.}$
$\displaystyle \hspace{0.2cm}\text{[ICSE 2014]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=\text{Rs. }800,\text{ no of months}=18,\text{ rate}=r\%,\text{ Maturity Amount}=\text{Rs. }15084$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 15084=800\times18+800\times\frac{18(18+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle r=\frac{(15084-800\times18)\times(2\times12)\times100}{800\times18\times19}\Rightarrow r=6\%$
$\\$

$\displaystyle \textbf{Question 18. }\text{A page from the saving account of Priyanka is given below:}$

$\displaystyle \begin{array}{|l|l|c|c|c|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)} \\ \hline \text{03/04/2006} & \text{B/F} & - & - & 4000.00 \\ \hline \text{05/04/2006} & \text{By Cash} & - & 2000.00 & 6000.00 \\ \hline \text{18/04/2006} & \text{By Cheque} & - & 6000.00 & 12000.00 \\ \hline \text{25/05/2006} & \text{To Cheque} & 5000.00 & - & 7000.00 \\ \hline \text{30/05/2006} & \text{By Cash} & - & 3000.00 & 10000.00 \\ \hline \text{20/07/2006} & \text{By Self} & 4000.00 & - & 6000.00 \\ \hline \text{10/09/2006} & \text{By Cash} & - & 2000.00 & 8000.00 \\ \hline \text{19/09/2006} & \text{To Cheque} & 1000.00 & - & 7000.00 \\ \hline \end{array}$

$\displaystyle \text{If the interest earned by Priyanka for the period ending September }2006\text{ is Rs. }175,\text{ find the rate of interest.}$
$\displaystyle \hspace{0.2cm}\text{[ICSE 2014]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Qualifying principal for various months:}$

$\displaystyle \begin{array}{|l|c|} \hline \text{Month} & \text{Principal (Rs.)} \\ \hline \text{April} & 6000 \\ \hline \text{May} & 7000 \\ \hline \text{June} & 10000 \\ \hline \text{July} & 6000 \\ \hline \text{August} & 6000 \\ \hline \text{September} & 7000 \\ \hline \text{Total} & 42000 \\ \hline \end{array}$

$\displaystyle P=\text{Rs. }42000,\text{ Rate}=r\%\text{ and }T=\frac{1}{12},\text{ Interest}=\text{Rs. }175$
$\displaystyle I=P\times R\times T$
$\displaystyle 175=42000\times\frac{r}{100}\times\frac{1}{12}\Rightarrow r=5\%$
$\\$

$\displaystyle \textbf{Question 19. }\text{Mr. Dhoni has an account in the Union Bank of India. The following entries are from his passbook:}$

$\displaystyle \text{Calculate the interest from January }2007\text{ to June }2007\text{ at the rate od }4\%\text{ per annum.}$
$\displaystyle \hspace{0.2cm}\text{[ICSE 2008]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Qualifying principal for various months:}$

$\displaystyle \begin{array}{|l|c|} \hline \text{Month} & \text{Principal (Rs.)} \\ \hline \text{January} & 2002 \\ \hline \text{February} & 2002 \\ \hline \text{March} & 2852 \\ \hline \text{April} & 1722 \\ \hline \text{May} & 2372 \\ \hline \text{June} & 1795 \\ \hline \text{Total} & 12745 \\ \hline \end{array}$

$\displaystyle P=\text{Rs. }12745,\text{ }R=4\%\text{ and }T=\frac{1}{12}$
$\displaystyle I=P\times R\times T=12745\times\frac{4}{100}\times\frac{1}{12}$
$\displaystyle =\text{Rs. }42.48$
$\\$

$\displaystyle \textbf{Question 20. }\text{Given below are the entries in a Saving Bank A/c passbook:}$

$\displaystyle \begin{array}{|l|l|c|c|c|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)} \\ \hline \text{Feb 8} & \text{B/F} & - & - & 8500 \\ \hline \text{Feb, 18} & \text{To Self} & 4000 & - & - \\ \hline \text{April, 12} & \text{By Cash} & - & 2238 & - \\ \hline \text{June, 15} & \text{To Self} & 5000 & - & - \\ \hline \text{June, 8} & \text{By Cash} & - & 6000 & - \\ \hline \end{array}$

$\displaystyle \text{Calculate the interest for the six months, February to July, at }4.5\%\text{ per annum on the minimum balance}$
$\displaystyle \text{on or after the }10\text{th day of each month.} \hspace{0.2cm}\text{[ICSE 2000, 2007]}$
$\displaystyle \text{Answer:}$

$\displaystyle \begin{array}{|l|l|c|c|c|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)} \\ \hline \text{Feb 8} & \text{B/F} & - & - & 8500 \\ \hline \text{Feb, 18} & \text{To Self} & 4000 & - & 4500 \\ \hline \text{April, 12} & \text{By Cash} & - & 2238 & 6738 \\ \hline \text{June, 15} & \text{To Self} & 5000 & - & 1738 \\ \hline \text{June, 8} & \text{By Cash} & - & 6000 & 7738 \\ \hline \end{array}$

$\displaystyle \text{Qualifying principal for various months:}$

$\displaystyle \begin{array}{|l|c|} \hline \text{Month} & \text{Principal (Rs.)} \\ \hline \text{February} & 4500 \\ \hline \text{March} & 4500 \\ \hline \text{April} & 4500 \\ \hline \text{May} & 6738 \\ \hline \text{June} & 1738 \\ \hline \text{July} & 7738 \\ \hline \text{Total} & 29714 \\ \hline \end{array}$

$\displaystyle P=\text{Rs. }29714,\text{ }R=4.5\%\text{ and }T=\frac{1}{12}$
$\displaystyle I=P\times R\times T=29714\times\frac{4.5}{100}\times\frac{1}{12}$
$\displaystyle =\text{Rs. }111.43$
$\\$

$\displaystyle \textbf{Question 21. }\text{Naveen deposits Rs. }800\text{ every month in a recurring deposit} \\ \text{account for }6\text{ months. If he receives Rs. }4884\text{ at the time of maturity, then} \\ \text{the interest he earns is:}$
$\displaystyle \text{(a) Rs. }84\qquad\text{(b) Rs. }42\qquad\text{(c) Rs. }24\qquad\text{(d) Rs. }284\qquad\text{[ICSE 2023]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Total amount deposited}=800\times6=\text{Rs. }4800$
$\displaystyle \text{Amount received at maturity}=\text{Rs. }4884$
$\displaystyle \text{Interest earned}=4884-4800=\text{Rs. }84$
$\displaystyle \therefore \text{The correct option is (a) Rs. }84.$
$\\$

$\displaystyle \textbf{Question 22. }\text{Mohit opened a recurring deposit account in a bank for }2\text{ years.} \\ \text{He deposits Rs. }1000\text{ every month and receives Rs. }25500\text{ on maturity. The interest} \\ \text{earned in }2\text{ years is:}$
$\displaystyle \text{(a) Rs. }13500\qquad\text{(b) Rs. }3000\qquad\text{(c) Rs. }24000\qquad\text{(d) Rs. }1500\qquad\text{[ICSE Semester I 2022]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Monthly deposit}=\text{Rs. }1000,\qquad \text{Time}=2\text{ years}=24\text{ months}$
$\displaystyle \text{Total amount deposited}=1000\times24=\text{Rs. }24000$
$\displaystyle \text{Maturity Value}=\text{Rs. }25500$
$\displaystyle \text{Interest earned}=25500-24000=\text{Rs. }1500$
$\displaystyle \therefore \text{The correct option is (d) Rs. }1500.$
$\\$

$\displaystyle \textbf{Question 23. }\text{A man deposited Rs. }500\text{ per month for }6\text{ months and} \\ \text{received Rs. }3300\text{ as the maturity value. The interest received by him is:}$
$\displaystyle \text{(a) Rs. }1950\qquad\text{(b) Rs. }300\qquad\text{(c) Rs. }2800\qquad\text{(d) None of these}\qquad\text{[ICSE Semester I 2022]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Monthly deposit}=\text{Rs. }500$
$\displaystyle \text{Total amount deposited in }6\text{ months}=500\times6=\text{Rs. }3000$
$\displaystyle \text{Maturity Value}=\text{Rs. }3300$
$\displaystyle \text{Interest earned}=3300-3000=\text{Rs. }300$
$\displaystyle \therefore \text{The correct option is (b) Rs. }300.$
$\\$

$\displaystyle \textbf{Question 24. }\text{A man deposited Rs. }1200\text{ every month in a recurring deposit} \\ \text{account for }1\text{ year at }5\%\text{ per annum simple interest. The interest earned by} \\ \text{him on maturity is:}$
$\displaystyle \text{(a) Rs. }14790\qquad\text{(b) Rs. }390\qquad\text{(c) Rs. }4680\qquad\text{(d) Rs. }780\qquad\text{[ICSE Semester I 2022]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Monthly deposit }(P)=\text{Rs. }1200,\qquad \text{Time}=1\text{ year}=12\text{ months},\qquad r=5\%$
$\displaystyle \text{Interest}=P\times\frac{n(n+1)}{2}\times\frac{r}{12\times100}$
$\displaystyle =1200\times\frac{12\times13}{2}\times\frac{5}{12\times100}$
$\displaystyle =\text{Rs. }390$
$\displaystyle \therefore \text{The correct option is (b) Rs. }390.$
$\\$

$\displaystyle \textbf{Question 25. }\text{Suresh has a recurring deposit account in a bank. He deposits Rs. }2000 \\ \text{ per month and the bank pays interest at the rate of }8\%\text{ per annum. If he gets Rs. }1040 \\ \text{ as interest at the time of maturity, find in years the total time for which} \\ \text{the account was held. [ICSE 2024]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Monthly deposit }(P)=\text{Rs. }2000,\qquad r=8\%\text{ p.a.},\qquad \text{Interest }(I)=\text{Rs. }1040$
$\displaystyle \text{For a recurring deposit account,}$
$\displaystyle I=P\times\frac{n(n+1)}{2}\times\frac{r}{12\times100}$
$\displaystyle 1040=2000\times\frac{n(n+1)}{2}\times\frac{8}{12\times100}$
$\displaystyle 1040=\frac{20}{3}\,n(n+1)$
$\displaystyle n(n+1)=\frac{1040\times3}{20}=156$
$\displaystyle 12\times13=156$
$\displaystyle \therefore n=12\text{ months}$
$\displaystyle =1\text{ year}$
$\displaystyle \text{Hence, the account was held for }1\text{ year.}$
$\\$

$\displaystyle \textbf{Question 26. }\text{Mr. Sonu has a recurring deposit account and deposits Rs. }750 \\ \text{ per month for }2\text{ years. If he gets Rs. }19125\text{ at the time of maturity, find} \\ \text{the rate of interest. [ICSE 2020]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Monthly deposit }(P)=\text{Rs. }750,\qquad \text{Time }(n)=2\text{ years}=24\text{ months}$
$\displaystyle \text{Maturity Value }(MV)=\text{Rs. }19125$
$\displaystyle \text{Let the rate of interest be }r\%\text{ per annum.}$
$\displaystyle MV=Pn\left(1+\frac{(n+1)r}{2400}\right)$
$\displaystyle 19125=750\times24\left(1+\frac{25r}{2400}\right)$
$\displaystyle 19125=18000\left(1+\frac{r}{96}\right)$
$\displaystyle 1+\frac{r}{96}=\frac{19125}{18000}$
$\displaystyle \frac{r}{96}=\frac{19125-18000}{18000}=\frac{1125}{18000}=\frac{1}{16}$
$\displaystyle r=96\times\frac{1}{16}=6$
$\displaystyle \text{Hence, the required rate of interest is }6\%\text{ per annum.}$
$\\$

$\displaystyle \textbf{Question 27. }\text{Amit deposits Rs. }1600\text{ per month in a bank for }18 \\ \text{ months in a recurring deposit account. If he gets Rs. }31080\text{ at the time of} \\ \text{maturity, what is the rate of interest per annum? [ICSE 2020]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Monthly deposit }(P)=\text{Rs. }1600,\qquad \text{Time }(n)=18\text{ months}$
$\displaystyle \text{Maturity Value }(MV)=\text{Rs. }31080$
$\displaystyle \text{Let the rate of interest be }r\%\text{ per annum.}$
$\displaystyle MV=Pn+\left(P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}\right)$
$\displaystyle 31080=1600\times18+\frac{1600\times18\times19}{2\times12}\times\frac{r}{100}$
$\displaystyle 31080-28800=\frac{1600\times18\times19}{2\times12}\times\frac{r}{100}$
$\displaystyle 2280=\frac{1600\times18\times19}{2\times12}\times\frac{r}{100}$
$\displaystyle r=\frac{2280\times2\times12\times100}{1600\times18\times19}$
$\displaystyle r=10\%$
$\displaystyle \text{Hence, the required rate of interest is }10\%\text{ per annum.}$
$\\$

$\displaystyle \textbf{Question 28. }\text{Rekha opened a recurring deposit account for }20\text{ months. The} \\ \text{rate of interest is }9\%\text{ per annum and Rekha receives Rs. }441\text{ as interest at the} \\ \text{time of maturity. Find the amount Rekha deposited each month. [ICSE 2019]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the monthly deposit be Rs. }P.$
$\displaystyle \text{Number of months }(n)=20,\qquad \text{Interest }(I)=\text{Rs. }441,\qquad r=9\%\text{ p.a.}$
$\displaystyle I=P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 441=P\times\frac{20\times21\times9}{2\times12\times100}$
$\displaystyle 441=P\times\frac{3780}{2400}$
$\displaystyle P=\frac{441\times2400}{3780}=\text{Rs. }280$
$\displaystyle \text{Hence, the amount deposited each month is Rs. }280.$
$\\$

$\displaystyle \textbf{Question 29. }\text{Priyanka has a recurring deposit account of Rs. }1000\text{ per month} \\ \text{at }10\%\text{ per annum. If she gets Rs. }5550\text{ as interest at the time of maturity, find the total} \\ \text{time for which the account was held. [ICSE 2018]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Given, monthly deposit }P=\text{Rs. }1000,\quad r=10\%,\quad I=\text{Rs. }5550$
$\displaystyle I=P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 5550=1000\times\frac{n(n+1)}{24}\times\frac{10}{100}$
$\displaystyle 5550=100\times\frac{n(n+1)}{24}$
$\displaystyle n(n+1)=\frac{5550\times24}{100}=1332$
$\displaystyle n^2+n-1332=0$
$\displaystyle n^2+37n-36n-1332=0$
$\displaystyle n(n+37)-36(n+37)=0$
$\displaystyle (n+37)(n-36)=0$
$\displaystyle n=-37\text{ or }n=36$
$\displaystyle \therefore n=36\text{ months}=3\text{ years}$
$\displaystyle \text{Hence, the account was held for }3\text{ years.}$
$\\$

$\displaystyle \textbf{Question 30. }\text{Sonia had a recurring deposit account in a bank and deposited} \\ \text{Rs. }600\text{ per month for }2\frac{1}{2}\text{ years. If the rate of interest was }10\%\text{ per annum, find the} \\ \text{maturity value of this account. [ICSE 2018]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Monthly deposit }(P)=\text{Rs. }600,\qquad r=10\%\text{ p.a.},\qquad n=2\frac{1}{2}\text{ years}=30\text{ months}$
$\displaystyle \text{Maturity Value }(MV)=Pn\left(1+\frac{(n+1)r}{2400}\right)$
$\displaystyle MV=600\times30\left(1+\frac{31\times10}{2400}\right)$
$\displaystyle =18000\left(1+\frac{31}{240}\right)$
$\displaystyle =18000\times\frac{271}{240}$
$\displaystyle =\text{Rs. }20325$
$\displaystyle \text{Hence, the maturity value of the recurring deposit account is Rs. }20325.$
$\\$

$\displaystyle \textbf{Question 31. }\text{Mr. Jacob has a }2\text{ year recurring deposit account in State Bank of} \\ \text{India and deposits Rs. }1500\text{ per month. If he receives Rs. }37875\text{ at the time} \\ \text{of maturity, find the rate of interest. [ICSE 2017]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Monthly deposit}=\text{Rs. }1500,\qquad \text{Time}=2\text{ years}=24\text{ months}$
$\displaystyle \text{Total amount deposited}=1500\times24=\text{Rs. }36000$
$\displaystyle \text{Maturity Value}=\text{Rs. }37875$
$\displaystyle \text{Interest earned}=37875-36000=\text{Rs. }1875$
$\displaystyle \text{For a recurring deposit account,}$
$\displaystyle I=P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 1875=\frac{1500\times24\times25}{2\times12}\times\frac{r}{100}$
$\displaystyle 1875=375\times r$
$\displaystyle r=\frac{1875}{375}=5\%$
$\displaystyle \text{Hence, the required rate of interest is }5\%\text{ per annum.}$
$\\$

$\displaystyle \textbf{Question 32. }\text{Mohan has a recurring deposit account in a bank for }2\text{ years} \\ \text{at }6\%\text{ per annum simple interest. If he gets Rs. }1200\text{ as interest at the} \\ \text{time of maturity, find:}$
$\displaystyle \text{(i) The monthly instalment.}$
$\displaystyle \text{(ii) The maturity amount. [ICSE 2016]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{(i) Given, }r=6\%\text{ p.a.},\qquad I=\text{Rs. }1200,\qquad n=2\text{ years}=24\text{ months}$
$\displaystyle I=P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 1200=\frac{P\times24\times25\times6}{2400}$
$\displaystyle P=\frac{1200\times2400}{24\times25\times6}=\text{Rs. }800$
$\displaystyle \therefore \text{The monthly instalment is Rs. }800.$
$\displaystyle \text{(ii) Maturity Amount}=P\times n+\text{Interest}$
$\displaystyle =800\times24+1200$
$\displaystyle =19200+1200=\text{Rs. }20400$
$\displaystyle \text{Hence, the maturity amount is Rs. }20400.$
$\\$

$\displaystyle \textbf{Question 33. }\text{Katrina opened a recurring deposit account with a nationalised bank} \\ \text{for a period of }2\text{ years. If the bank pays interest at the rate of }6\%\text{ per annum and} \\ \text{the monthly instalment is Rs. }1000,\text{ find:}$
$\displaystyle \text{(i) Interest earned in }2\text{ years.}$
$\displaystyle \text{(ii) Maturity value. [ICSE 2015]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Given, monthly deposit }(P)=\text{Rs. }1000,\qquad n=2\text{ years}=24\text{ months},\qquad r=6\%\text{ p.a.}$
$\displaystyle \text{(i) Interest}=P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle =1000\times\frac{24\times25}{2\times12}\times\frac{6}{100}$
$\displaystyle =\text{Rs. }1500$
$\displaystyle \text{(ii) Maturity Value}=P\times n+\text{Interest}$
$\displaystyle =1000\times24+1500$
$\displaystyle =24000+1500$
$\displaystyle =\text{Rs. }25500$
$\displaystyle \text{Hence, the interest earned is Rs. }1500\text{ and the maturity value is Rs. }25500.$
$\\$

$\displaystyle \textbf{Question 34. }\text{Shahrukh opened a recurring deposit account in a bank and deposited} \\ \text{Rs. }800\text{ per month for }1\frac{1}{2}\text{ years. If he received Rs. }15084\text{ at the time} \\ \text{of maturity, find the rate of interest per annum. [ICSE 2014]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Monthly deposit }(P)=\text{Rs. }800,\qquad n=1\frac{1}{2}\text{ years}=18\text{ months}$
$\displaystyle \text{Maturity Value }(MV)=\text{Rs. }15084$
$\displaystyle \text{Let the rate of interest be }r\%\text{ per annum.}$
$\displaystyle I=P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle =\frac{800\times18\times19}{2\times12}\times\frac{r}{100}$
$\displaystyle =114r$
$\displaystyle \text{Total amount deposited}=800\times18=\text{Rs. }14400$
$\displaystyle \text{Maturity Value}=\text{Total amount deposited}+\text{Interest}$
$\displaystyle 15084=14400+114r$
$\displaystyle 114r=15084-14400=684$
$\displaystyle r=\frac{684}{114}=6\%$
$\displaystyle \text{Hence, the required rate of interest is }6\%\text{ per annum.}$
$\\$

$\displaystyle \textbf{Question 35. }\text{Mr. Britto deposits a certain sum of money each month in a recurring} \\ \text{deposit account of a bank. If the rate of interest is }8\%\text{ per annum and Mr. Britto gets} \\ \text{Rs. }8088\text{ from the bank after }3\text{ years, find the value of his monthly} \\ \text{instalment. [ICSE 2013]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Given, }r=8\%\text{ p.a.},\qquad MV=\text{Rs. }8088,\qquad n=3\text{ years}=36\text{ months}$
$\displaystyle \text{Let the monthly instalment be Rs. }P.$
$\displaystyle MV=Pn+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 8088=36P+\frac{P\times36\times37}{2\times12}\times\frac{8}{100}$
$\displaystyle 8088=36P+\frac{10656P}{2400}$
$\displaystyle 8088=\frac{86400P+10656P}{2400}$
$\displaystyle 8088=\frac{97056P}{2400}$
$\displaystyle P=\frac{8088\times2400}{97056}=\text{Rs. }200$
$\displaystyle \text{Hence, the monthly instalment is Rs. }200.$
$\\$

$\displaystyle \textbf{Question 36. }\text{Kiran deposited Rs. }200\text{ per month for }36\text{ months in} \\ \text{a recurring deposit account. If the bank pays interest at the rate of }11\%\text{ per annum,} \\ \text{find the amount she gets on maturity. [ICSE 2012]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Monthly deposit }(P)=\text{Rs. }200,\qquad n=36\text{ months},\qquad r=11\%\text{ p.a.}$
$\displaystyle \text{Interest}=P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle =\frac{200\times36\times37}{2\times12}\times\frac{11}{100}$
$\displaystyle =\text{Rs. }1221$
$\displaystyle \text{Total amount deposited}=200\times36=\text{Rs. }7200$
$\displaystyle \text{Maturity Amount}=7200+1221=\text{Rs. }8421$
$\displaystyle \text{Hence, Kiran will receive Rs. }8421\text{ on maturity.}$
$\\$

$\displaystyle \textbf{Question 37. }\text{Ahmed has a recurring deposit account in a bank. He deposits} \\ \text{Rs. }2500\text{ per month for }2\text{ years. If he gets Rs. }66250\text{ at the time of} \\ \text{maturity, find:}$
$\displaystyle \text{(i) The interest paid by the bank.}$
$\displaystyle \text{(ii) The rate of interest. [ICSE 2011]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Given, monthly deposit }(P)=\text{Rs. }2500,\qquad n=2\text{ years}=24\text{ months}$
$\displaystyle \text{Maturity Value }(MV)=\text{Rs. }66250$
$\displaystyle \text{(i) Total amount deposited}=2500\times24=\text{Rs. }60000$
$\displaystyle \text{Interest earned}=66250-60000=\text{Rs. }6250$
$\displaystyle \text{(ii) Let the rate of interest be }r\%\text{ per annum.}$
$\displaystyle I=P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 6250=\frac{2500\times24\times25}{2\times12}\times\frac{r}{100}$
$\displaystyle 6250=625r$
$\displaystyle r=\frac{6250}{625}=10\%$
$\displaystyle \text{Hence, (i) the interest paid by the bank is Rs. }6250\text{ and (ii) the rate of interest is }10\%\text{ per annum.}$
$\\$

$\displaystyle \textbf{Question 38. }\text{David opened a recurring deposit account in a bank and deposited} \\ \text{Rs. }300\text{ per month for }2\text{ years. If he received Rs. }7725\text{ at the time of maturity,} \\ \text{find the rate of interest per annum. [ICSE 2008]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Monthly deposit }(P)=\text{Rs. }300,\qquad n=2\text{ years}=24\text{ months},\qquad MV=\text{Rs. }7725$
$\displaystyle \text{Let the rate of interest be }r\%\text{ per annum.}$
$\displaystyle MV=Pn+\frac{P\times n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle =Pn\left(1+\frac{(n+1)r}{2400}\right)$
$\displaystyle 7725=300\times24\left(1+\frac{25r}{2400}\right)$
$\displaystyle 7725=7200\left(\frac{2400+25r}{2400}\right)$
$\displaystyle \frac{7725}{7200}=\frac{2400+25r}{2400}$
$\displaystyle \frac{103}{96}=\frac{2400+25r}{2400}$
$\displaystyle 103\times25=2400+25r$
$\displaystyle 2575=2400+25r$
$\displaystyle 25r=175$
$\displaystyle r=7\%$
$\displaystyle \text{Hence, the required rate of interest is }7\%\text{ per annum.}$
$\\$

$\displaystyle \textbf{Question 39. }\text{Saloni deposited Rs. }150\text{ per month in her bank for }8\text{ months} \\ \text{under the recurring deposit scheme. What will be the maturity value of her deposit, if} \\ \text{the rate of interest is }8\%\text{ per annum and the interest is calculated} \\ \text{at the end of every month? [ICSE 2007, 2001]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Monthly deposit }(P)=\text{Rs. }150,\qquad n=8\text{ months},\qquad r=8\%\text{ p.a.}$
$\displaystyle \text{Maturity Value }(MV)=Pn+\text{Interest}$
$\displaystyle =Pn+\frac{P\times n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle =Pn\left(1+\frac{(n+1)r}{2400}\right)$
$\displaystyle MV=150\times8\left(1+\frac{9\times8}{2400}\right)$
$\displaystyle =1200\left(1+\frac{72}{2400}\right)$
$\displaystyle =1200\left(1+\frac{3}{100}\right)$
$\displaystyle =1200\times\frac{103}{100}$
$\displaystyle =\text{Rs. }1236$
$\displaystyle \text{Hence, the maturity value of the recurring deposit account is Rs. }1236.$
$\\$

$\displaystyle \textbf{Question 40. }\text{Salman deposits Rs. }1000\text{ every month in a recurring deposit} \\ \text{account for }2\text{ years. If he receives Rs. }26000\text{ on maturity, find:}$
$\displaystyle \text{(i) The total interest earned by Salman.}$
$\displaystyle \text{(ii) The rate of interest. [ICSE 2023]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Monthly deposit}=\text{Rs. }1000,\qquad \text{Time}=2\text{ years}=24\text{ months}$
$\displaystyle \text{Total amount deposited}=1000\times24=\text{Rs. }24000$
$\displaystyle \text{Maturity Value}=\text{Rs. }26000$
$\displaystyle \text{(i) Interest earned}=26000-24000=\text{Rs. }2000$
$\displaystyle \text{(ii) Let the rate of interest be }r\%\text{ per annum.}$
$\displaystyle I=P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 2000=1000\times\frac{24\times25}{2\times12}\times\frac{r}{100}$
$\displaystyle 2000=250r$
$\displaystyle r=\frac{2000}{250}=8\%$
$\displaystyle \text{Hence, (i) the total interest earned is Rs. }2000\text{ and (ii) the rate of interest is }8\%\text{ per annum.}$
$\\$

$\displaystyle \textbf{Question 41. }\text{Salman deposits Rs. }1200\text{ every month in a recurring deposit} \\ \text{account for }2\frac{1}{2}\text{ years. If the rate of interest is }6\%\text{ per annum, find the amount} \\ \text{he will receive on maturity. [ICSE 2023]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Monthly deposit }(P)=\text{Rs. }1200,\qquad n=2\frac{1}{2}\text{ years}=30\text{ months},\qquad r=6\%\text{ p.a.}$
$\displaystyle \text{Maturity Value}=Pn+\frac{P\times n(n+1)\times r}{2400}$
$\displaystyle =Pn\left(1+\frac{(n+1)r}{2400}\right)$
$\displaystyle =1200\times30\left(1+\frac{31\times6}{2400}\right)$
$\displaystyle =36000\left(1+\frac{31}{400}\right)$
$\displaystyle =36000\left(\frac{431}{400}\right)$
$\displaystyle =90\times431$
$\displaystyle =\text{Rs. }38790$
$\displaystyle \text{Hence, Salman will receive Rs. }38790\text{ on maturity.}$
$\\$

$\displaystyle \textbf{Question 42. }\text{Mr. Richard has a recurring deposit account in a bank for }3\text{ years} \\ \text{at }7.5\%\text{ per annum simple interest. If he gets Rs. }8325\text{ as interest at the} \\ \text{time of maturity, find:}$
$\displaystyle \text{(i) The monthly deposit.}$
$\displaystyle \text{(ii) The maturity value. [ICSE 2017]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Given, }n=3\text{ years}=36\text{ months},\qquad r=7.5\%\text{ p.a.},\qquad I=\text{Rs. }8325$
$\displaystyle \text{(i) Let the monthly deposit be Rs. }P.$
$\displaystyle \text{Maturity Value }(MV)=36P+8325\qquad\cdots(1)$
$\displaystyle \text{Also, }MV=36P\left(1+\frac{(36+1)\times7.5}{2400}\right)\qquad\cdots(2)$
$\displaystyle \text{From (1) and (2),}$
$\displaystyle 36P+8325=36P\left(1+\frac{37\times7.5}{2400}\right)$
$\displaystyle =36P\left(\frac{357}{320}\right)$
$\displaystyle 36P\left(\frac{357}{320}-1\right)=8325$
$\displaystyle 36P\left(\frac{37}{320}\right)=8325$
$\displaystyle P=\frac{8325\times320}{36\times37}=\text{Rs. }2000$
$\displaystyle \therefore \text{The monthly deposit is Rs. }2000.$
$\displaystyle \text{(ii) Maturity Value}=36\times2000+8325$
$\displaystyle =72000+8325$
$\displaystyle =\text{Rs. }80325$
$\displaystyle \text{Hence, the maturity value is Rs. }80325.$
$\\$

$\displaystyle \textbf{Question 43. }\text{On a certain sum of money, the difference between the compound interest} \\ \text{for a year, payable half-yearly, and the simple interest for a year is Rs. }16.\text{ Find the} \\ \text{sum lent out, if the rate of interest in both cases is }8\%.\text{ [ICSE 2017]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the principal be Rs. }P.$
$\displaystyle \text{Simple Interest}=\frac{P\times8\times1}{100}=\frac{8P}{100}$
$\displaystyle \text{For compound interest payable half-yearly, rate per half-year}=\frac{8}{2}=4\%$
$\displaystyle \text{Number of half-years}=2$
$\displaystyle \text{Compound Interest}=P\left[\left(1+\frac{4}{100}\right)^2-1\right]$
$\displaystyle =P\left[\left(\frac{26}{25}\right)^2-1\right]$
$\displaystyle =P\left(\frac{676-625}{625}\right)=\frac{51P}{625}$
$\displaystyle \text{Given, }CI-SI=16$
$\displaystyle \frac{51P}{625}-\frac{8P}{100}=16$
$\displaystyle \frac{204P-200P}{2500}=16$
$\displaystyle \frac{4P}{2500}=16$
$\displaystyle P=\frac{16\times2500}{4}=\text{Rs. }10000$
$\displaystyle \text{Hence, the sum lent out is Rs. }10000.$
$\\$

Question 44 : Mr. A Ramchandra has an account with Central Bank of India. The following entries are from his passbook:
$\displaystyle \text{Complete the passbook given below}$
$\displaystyle \begin{array}{|c|l|c|c|c|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (in Rs)} & \text{Deposits (in Rs)} & \text{Balance (in Rs)}\\ \hline 05\ \text{Jan 2009} & \text{B/F} & & & 8000\\ \hline 20\ \text{Jan 2009} & \text{To self} & 2500 & & 5500\\ \hline 04\ \text{Feb 2009} & \text{By cash} & & 9000 & 14500\\ \hline 20\ \text{Feb 2009} & \text{By cash} & & 3000 & 17500\\ \hline 04\ \text{Mar 2009} & \text{To self} & 1000 & & 16500\\ \hline 15\ \text{Apr 2009} & \text{By cash} & & 12000 & 28500\\ \hline \end{array}$

Complete the above page of his passbook and calculate the interest accumulated in four months, January to April at the rate of 3.5% per annum.
If the interest is added on 30th April, then find his balance on that date. [ICSE 2017]
$\displaystyle \text{Answer:}$
$\displaystyle \text{Complete the passbook given below}$
$\displaystyle \begin{array}{|c|l|c|c|c|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (in Rs)} & \text{Deposits (in Rs)} & \text{Balance (in Rs)}\\ \hline 05\ \text{Jan 2009} & \text{B/F} & & & 8000\\ \hline 20\ \text{Jan 2009} & \text{To self} & 2500 & & 5500\\ \hline 04\ \text{Feb 2009} & \text{By cash} & & 9000 & 14500\\ \hline 20\ \text{Feb 2009} & \text{By cash} & & 3000 & 17500\\ \hline 04\ \text{Mar 2009} & \text{To self} & 1000 & & 16500\\ \hline 15\ \text{Apr 2009} & \text{By cash} & & 12000 & 28500\\ \hline \end{array}$
$\displaystyle \text{Table for minimum balance for qualifying amount}$
$\displaystyle \begin{array}{|c|c|} \hline \text{Months} & \text{Minimum balance between 10th day and the last day}\\ \hline \text{Jan} & 5500\\ \hline \text{Feb} & 14500\\ \hline \text{March} & 16500\\ \hline \text{April} & 16500\\ \hline \text{Total} & 53000\\ \hline \end{array}$
$\displaystyle \text{Here, principal for 1 month}=\text{Rs }53000$
$\displaystyle \text{Given, rate of interest, }R=3.5\%\ \text{per annum}$
$\displaystyle \therefore\ \text{Interest}=\frac{P \times R \times T}{100}=\frac{53000 \times 3.5 \times 1}{100 \times 12}$
$\displaystyle =\frac{1855}{12}=\text{Rs }154.58$
$\displaystyle \therefore\ \text{Balance on date 30th April}=\text{Rs }(28500+154.58)$
$\displaystyle =\text{Rs }28654.58$

Question 45 : Joseph has a recurring deposit account in a bank for 2 yr at the rate of 8% per annum simple interest. [ICSE Semester–I 2022]

(i) If at the time of maturity Joseph receives $\displaystyle \text{Rs }2000$
as interest, then the monthly instalment is:
(a) $\displaystyle \text{Rs }1200$
(b) $\displaystyle \text{Rs }600$
(c) $\displaystyle \text{Rs }1000$
(d) $\displaystyle \text{Rs }1600$

(ii) The total amount deposited in the bank is:
(a) $\displaystyle \text{Rs }25000$
(b) $\displaystyle \text{Rs }24000$
(c) $\displaystyle \text{Rs }26000$
(d) $\displaystyle \text{Rs }23000$

(iii) The amount Joseph receives on maturity is:
(a) $\displaystyle \text{Rs }27000$
(b) $\displaystyle \text{Rs }25000$
(c) $\displaystyle \text{Rs }26000$
(d) $\displaystyle \text{Rs }28000$

(iv) If the monthly instalment is $\displaystyle \text{Rs }100$ and the rate
of interest is 8%, in how many months Joseph will receive
$\displaystyle \text{Rs }52$ as interest?
(a) 18
(b) 30
(c) 12
(d) 6
$\displaystyle \text{Answer:}$
$\displaystyle \text{Given, rate of interest }(r)=8\%\ \text{per annum}$
$\displaystyle \text{Number of month }(n)=24\ \text{months}$
$\displaystyle (i)\ (c)\ \text{Interest }(I)=\text{Rs }2000$
$\displaystyle \therefore\ I=\frac{P n(n+1) \times r}{2400}$
$\displaystyle \Rightarrow 2000=\frac{P \times 24 \times 25 \times 8}{2400}$
$\displaystyle \Rightarrow P=\frac{2000 \times 2400}{25 \times 8 \times 24}=\text{Rs }1000$
$\displaystyle (ii)\ (b)\ \text{Monthly instalment}=\text{Rs }1000$
$\displaystyle \text{Time period }2\ \text{yr or }24\ \text{months}$
$\displaystyle \therefore\ \text{Total amount deposit}=\text{Total month} \times \text{Monthly instalment}$
$\displaystyle =24 \times 1000=\text{Rs }24000$
$\displaystyle (iii)\ (c)\ \text{Maturity amount}=\text{Total amount deposit}+\text{Interest}$
$\displaystyle =\text{Rs }(24000+2000)=\text{Rs }26000$
$\displaystyle (iv)\ (c)\ \text{Given, monthly instalment }(P)=\text{Rs }100$
$\displaystyle \text{and rate of interest }(r)=8\%$
$\displaystyle \text{and Interest}=\text{Rs }52$
$\displaystyle \therefore\ I=\frac{P n(n+1) \times r}{2400}$
$\displaystyle \Rightarrow 52=\frac{100 \times 8 \times n(n+1)}{2400}$
$\displaystyle \Rightarrow 52 \times 3=n(n+1)$
$\displaystyle \Rightarrow n^2+n-156=0$
$\displaystyle \Rightarrow n^2+13n-12n-156=0$
$\displaystyle \Rightarrow n(n+13)-12(n+13)=0$
$\displaystyle \Rightarrow (n-12)(n+13)=0$
$\displaystyle \Rightarrow n=12,-13$
$\displaystyle \text{Month cannot be negative.}$
$\displaystyle \text{So, number of month is }12.$

$\displaystyle \textbf{Question 46. }\text{The difference between the compound interest for a year payable half-yearly}$
$\displaystyle \text{and the simple interest on a certain sum of money lent out at }10\%\text{ per annum for a }$
$\displaystyle \text{year is Rs }15. \text{ Find the sum of money.}\hspace{0.2cm}\text{[ICSE 1998]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the principal be Rs }P.$
$\displaystyle \text{Rate of interest}=10\%\text{ p.a.}$
$\displaystyle \text{For half-yearly compounding, rate per half-year}=5\%$
$\displaystyle \text{Number of half-years}=2$
$\displaystyle \text{Compound Interest}=P\left(1+\frac{5}{100}\right)^{2}-P$
$\displaystyle =P\left(\frac{105}{100}\right)^{2}-P$
$\displaystyle =P\left(\frac{11025}{10000}-1\right)$
$\displaystyle =P\left(\frac{1025}{10000}\right)$
$\displaystyle =0.1025P$
$\displaystyle \text{Simple Interest}=P\times\frac{10\times1}{100}=0.1P$
$\displaystyle \text{Difference between C.I. and S.I.}=0.1025P-0.1P$
$\displaystyle =0.0025P$
$\displaystyle 0.0025P=15$
$\displaystyle P=\frac{15}{0.0025}$
$\displaystyle =6000$
$\displaystyle \therefore \text{The sum of money}= \text{Rs }6000$
$\\$

$\displaystyle \textbf{Question 47. }\text{Nikita invests Rs }6000\text{ for two years at a certain rate of interest compounded}$
$\displaystyle \text{annually. At the end of first year it amounts to Rs }6720.\text{ Calculate}$
$\displaystyle \text{(i) the rate of interest.}$
$\displaystyle \text{(ii) the amount at the end of the second year.}\hspace{0.2cm}\text{[ICSE 2010]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=6000,\quad A=6720,\quad T=1\text{ year}$
$\displaystyle \text{Interest for first year}=6720-6000=720$
$\displaystyle R=\frac{720}{6000}\times100=12\%$
$\displaystyle \text{Amount at the end of second year}=6720\left(1+\frac{12}{100}\right)$
$\displaystyle =6720\times1.12$
$\displaystyle =7526.40$
$\displaystyle \therefore \text{Rate of interest}=12\%\text{ and amount at the end of second year}=\text{Rs }7526.40$
$\\$

$\displaystyle \textbf{Question 48. }\text{At what rate percent per annum compound interest, would Rs }80000\text{ amount}$
$\displaystyle \text{to Rs }88200\text{ in two years, interest being compounded yearly?}\hspace{0.2cm}\text{[ICSE 1993]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=80000,\quad A=88200,\quad T=2\text{ years}$
$\displaystyle A=P\left(1+\frac{R}{100}\right)^{2}$
$\displaystyle 88200=80000\left(1+\frac{R}{100}\right)^{2}$
$\displaystyle \left(1+\frac{R}{100}\right)^{2}=\frac{88200}{80000}$
$\displaystyle =1.1025$
$\displaystyle 1+\frac{R}{100}=1.05$
$\displaystyle \frac{R}{100}=0.05$
$\displaystyle R=5\%$
$\displaystyle \therefore \text{Rate of interest}=5\%\text{ p.a.}$
$\\$

$\displaystyle \textbf{Question 49. }\text{A certain sum of money amounts to Rs }5292\text{ in two years and Rs }5556.60\text{ in}$
$\displaystyle \text{three years, interest being compounded annually. Find the rate percent.}\hspace{0.2cm}\text{[ICSE 1994]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Amount after }2\text{ years}=5292$
$\displaystyle \text{Amount after }3\text{ years}=5556.60$
$\displaystyle \text{Interest for third year}=5556.60-5292=264.60$
$\displaystyle R=\frac{264.60}{5292}\times100$
$\displaystyle =5\%$
$\displaystyle \therefore \text{Rate of interest}=5\%\text{ p.a.}$
$\\$

$\displaystyle \textbf{Question 50. }\text{A person invests Rs }5600\text{ at }14\%\text{ p.a. compound interest for }2\text{ years. Calculate}$
$\displaystyle \text{(i) the interest for the 1st year,}$
$\displaystyle \text{(ii) the amount at the end of the first year,}$
$\displaystyle \text{(iii) the interest for second year, correct to the nearest rupee.}\hspace{0.2cm}\text{[ICSE 1997]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=5600,\quad R=14\%$
$\displaystyle \text{(i) Interest for first year}=\frac{5600\times14\times1}{100}$
$\displaystyle =784$
$\displaystyle \therefore \text{Interest for first year}=\text{Rs }784$
$\displaystyle \text{(ii) Amount at the end of first year}=5600+784$
$\displaystyle =6384$
$\displaystyle \therefore \text{Amount at the end of first year}=\text{Rs }6384$
$\displaystyle \text{(iii) Interest for second year}=\frac{6384\times14}{100}$
$\displaystyle =893.76$
$\displaystyle \approx894$
$\displaystyle \therefore \text{Interest for second year}=\text{Rs }894$
$\\$

$\displaystyle \textbf{Question 51. }\text{A person invests Rs }10000\text{ for two years at a certain rate of interest}$
$\displaystyle \text{compounded annually. At the end of one year this sum amounts to Rs }12000.$
$\displaystyle \text{Calculate:}$
$\displaystyle \text{(i) the rate of interest per annum} \hspace{0.2cm}\text{[ICSE 2006]}$
$\displaystyle \text{(ii) the amount at the end of the second year}$
$\displaystyle \text{Answer:}$
$\displaystyle P=10000,\quad A=12000$
$\displaystyle \text{Interest for first year}=12000-10000=2000$
$\displaystyle R=\frac{2000}{10000}\times100$
$\displaystyle =20\%$
$\displaystyle \therefore \text{Rate of interest}=20\%\text{ p.a.}$
$\displaystyle \text{Amount at the end of second year}=12000\left(1+\frac{20}{100}\right)$
$\displaystyle =12000\times1.2$
$\displaystyle =14400$
$\displaystyle \therefore \text{Amount at the end of second year}=\text{Rs }14400$
$\\$

$\displaystyle \textbf{Question 52. }\text{A sum of Rs }9600\text{ is invested for }3\text{ years at }10\%\text{ per annum at compound}$
$\displaystyle \text{interest.} \hspace{0.2cm}\text{[ICSE 1996]}$
$\displaystyle \text{(i) What is the sum due at the end of the first year ?}$
$\displaystyle \text{(ii) What is the sum due at the end of the second year ?}$
$\displaystyle \text{(iii) Find the compound interest earned in }2\text{ years ?}$
$\displaystyle \text{(iv) Find the difference between the answers in (ii) and (i) and find the interest}$
$\displaystyle \text{on this sum for one year.}$
$\displaystyle \text{(v) Hence write down the compound interest for the third year.}$
$\displaystyle \text{Answer:}$
$\displaystyle P=9600,\quad R=10\%$
$\displaystyle \text{(i) Amount after first year}=9600\left(1+\frac{10}{100}\right)$
$\displaystyle =10560$
$\displaystyle \therefore \text{Sum due at the end of first year}=\text{Rs }10560$
$\displaystyle \text{(ii) Amount after second year}=10560\left(1+\frac{10}{100}\right)$
$\displaystyle =11616$
$\displaystyle \therefore \text{Sum due at the end of second year}=\text{Rs }11616$
$\displaystyle \text{(iii) Compound interest in }2\text{ years}=11616-9600$
$\displaystyle =2016$
$\displaystyle \therefore \text{Compound interest earned in }2\text{ years}=\text{Rs }2016$
$\displaystyle \text{(iv) Difference between (ii) and (i)}=11616-10560$
$\displaystyle =1056$
$\displaystyle \text{Interest on this sum for one year at }10\%$
$\displaystyle =\frac{1056\times10}{100}=105.60$
$\displaystyle \therefore \text{Interest}= \text{Rs }105.60$
$\displaystyle \text{(v) Compound interest for third year}=1056+105.60$
$\displaystyle =1161.60$
$\displaystyle \therefore \text{Compound interest for third year}= \text{Rs }1161.60$
$\\$

$\displaystyle \textbf{Question 53. }\text{A man invests Rs }5000\text{ for three years at a certain rate of interest,}$
$\displaystyle \text{compounded annually. At the end of the first year it amounts to Rs }5600.$
$\displaystyle \text{Calculate} \hspace{0.2cm}\text{[ICSE 1999]}$
$\displaystyle \text{(i) the rate of interest per annum.}$
$\displaystyle \text{(ii) the interest accrued in the second year.}$
$\displaystyle \text{(iii) the amount at the end of the third year.}$
$\displaystyle \text{Answer:}$
$\displaystyle P=5000,\quad A=5600$
$\displaystyle \text{Interest for first year}=5600-5000=600$
$\displaystyle R=\frac{600}{5000}\times100=12\%$
$\displaystyle \therefore \text{Rate of interest}=12\%\text{ p.a.}$
$\displaystyle \text{Interest in second year}=\frac{5600\times12}{100}$
$\displaystyle =672$
$\displaystyle \therefore \text{Interest accrued in second year}= \text{Rs }672$
$\displaystyle \text{Amount at the end of third year}=5000\left(1+\frac{12}{100}\right)^{3}$
$\displaystyle =5000(1.12)^{3}$
$\displaystyle =7024.64$
$\displaystyle \therefore \text{Amount at the end of third year}= \text{Rs }7024.64$
$\\$

$\displaystyle \textbf{Question 54. }\text{Calculate the compound interest for the second year on Rs }8000\text{ invested}$
$\displaystyle \text{for }3\text{ years at }10\%\text{ p.a.} \hspace{0.2cm}\text{[ICSE 2000]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Amount at the end of first year}=8000\left(1+\frac{10}{100}\right)$
$\displaystyle =8800$
$\displaystyle \text{Interest for second year}=\frac{8800\times10}{100}$
$\displaystyle =880$
$\displaystyle \therefore \text{Compound interest for the second year}= \text{Rs }880$
$\\$

$\displaystyle \textbf{Question 55. }\text{A man borrows Rs }5000\text{ at }12\%\text{ compound interest per annum, interest}$
$\displaystyle \text{payable every six months. He pays back Rs }1800\text{ at the end of every six}$
$\displaystyle \text{months. Calculate the third payment he has to make at the end of }18\text{ months}$
$\displaystyle \text{in order to clear the entire loan.}\hspace{0.2cm}\text{[ICSE 2001]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Rate for }6\text{ months}=6\%$
$\displaystyle \text{Amount due after first }6\text{ months}=5000\left(1+\frac{6}{100}\right)$
$\displaystyle =5300$
$\displaystyle \text{Balance after first payment}=5300-1800=3500$
$\displaystyle \text{Amount due after next }6\text{ months}=3500\left(1+\frac{6}{100}\right)$
$\displaystyle =3710$
$\displaystyle \text{Balance after second payment}=3710-1800=1910$
$\displaystyle \text{Amount due after next }6\text{ months}=1910\left(1+\frac{6}{100}\right)$
$\displaystyle =2024.60$
$\displaystyle \therefore \text{Third payment}= \text{Rs }2024.60$
$\\$

$\displaystyle \textbf{Question 56. }\text{On a certain sum of money, the difference between the compound interest for}$
$\displaystyle \text{a year, payable half-yearly, and the simple interest for a year is Rs }180.$
$\displaystyle \text{Find the sum lent out, if the rate of interest in both the cases is }10\%. \hspace{0.2cm}\text{[ICSE 2002]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the principal be Rs }P.$
$\displaystyle \text{Rate for half-year}=5\%$
$\displaystyle \text{Compound interest}=P\left(1+\frac{5}{100}\right)^{2}-P$
$\displaystyle =P\left[\left(\frac{21}{20}\right)^{2}-1\right]$
$\displaystyle =P\left(\frac{441}{400}-1\right)=\frac{41P}{400}$
$\displaystyle \text{Simple interest}=P\times\frac{10}{100}=\frac{P}{10}$
$\displaystyle \text{Difference}=\frac{41P}{400}-\frac{P}{10}$
$\displaystyle =\frac{41P-40P}{400}=\frac{P}{400}$
$\displaystyle \frac{P}{400}=180$
$\displaystyle P=72000$
$\displaystyle \therefore \text{Sum lent out}= \text{Rs }72000$
$\\$

$\displaystyle \textbf{Question 57. }\text{The compound interest on a certain sum of money at }5\%\text{ per annum for two}$
$\displaystyle \text{years is Rs }246.\text{ Calculate the simple interest on the same sum for three years}$
$\displaystyle \text{at }6\%\text{ per annum.}\hspace{0.2cm}\text{[ICSE 2004]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the principal be Rs }P.$
$\displaystyle \text{C.I. for }2\text{ years}=P\left[\left(1+\frac{5}{100}\right)^{2}-1\right]$
$\displaystyle =P\left[\left(\frac{21}{20}\right)^{2}-1\right]$
$\displaystyle =P\left(\frac{441}{400}-1\right)=\frac{41P}{400}$
$\displaystyle \frac{41P}{400}=246$
$\displaystyle P=\frac{246\times400}{41}=2400$
$\displaystyle \text{Simple interest for }3\text{ years at }6\%=\frac{2400\times6\times3}{100}$
$\displaystyle =432$
$\displaystyle \therefore \text{Simple interest}= \text{Rs }432$
$\\$

$\displaystyle \textbf{Question 58. }\text{If the interest is compounded half-yearly, calculate the amount when the}$
$\displaystyle \text{principal is Rs }7400,\text{ the rate of interest is }5\%\text{ per annum and the duration is}$
$\displaystyle \text{one year.}\hspace{0.2cm}\text{[ICSE 2005]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=7400,\quad R=5\%\text{ p.a.},\quad T=1\text{ year}$
$\displaystyle \text{Rate for half-year}=\frac{5}{2}\%=2.5\%$
$\displaystyle \text{Number of half-years}=2$
$\displaystyle A=P\left(1+\frac{2.5}{100}\right)^{2}$
$\displaystyle =7400\left(1+\frac{1}{40}\right)^{2}$
$\displaystyle =7400\left(\frac{41}{40}\right)^{2}$
$\displaystyle =7400\times\frac{1681}{1600}$
$\displaystyle =7774.625$
$\displaystyle \therefore \text{Amount}= \text{Rs }7774.625\approx \text{Rs }7775$
$\\$

$\displaystyle \textbf{Question 59. }\text{A sum of money is lent out at compound interest for }2\text{ years at }20\%\text{ p.a.,}$
$\displaystyle \text{C.I. being reckoned yearly. If the same sum of money was lent out at compound}$
$\displaystyle \text{interest at the same rate per annum, C.I. being reckoned half-yearly, it would}$
$\displaystyle \text{have fetched Rs }482\text{ more by the way of interest. Calculate the sum of money}$
$\displaystyle \text{lent out.}\hspace{0.2cm}\text{[ICSE 1992]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the principal be Rs }P.$
$\displaystyle \text{Amount when compounded yearly}=P\left(1+\frac{20}{100}\right)^{2}$
$\displaystyle =P(1.2)^{2}=1.44P$
$\displaystyle \text{C.I. when compounded yearly}=1.44P-P=0.44P$
$\displaystyle \text{For half-yearly compounding, rate}=10\%\text{ and number of periods}=4$
$\displaystyle \text{Amount when compounded half-yearly}=P\left(1+\frac{10}{100}\right)^{4}$
$\displaystyle =P(1.1)^{4}=1.4641P$
$\displaystyle \text{C.I. when compounded half-yearly}=1.4641P-P=0.4641P$
$\displaystyle \text{Difference}=0.4641P-0.44P=0.0241P$
$\displaystyle 0.0241P=482$
$\displaystyle P=\frac{482}{0.0241}=20000$
$\displaystyle \therefore \text{Sum of money lent out}= \text{Rs }20000$
$\\$

$\displaystyle \textbf{Question 60. }\text{The simple interest on a sum of money for }2\text{ years at }4\%\text{ per annum is}$
$\displaystyle \text{Rs }340.\text{ Find (i) the sum of money and (ii) the compound interest on this sum}$
$\displaystyle \text{for one year payable half-yearly at the same rate.}\hspace{0.2cm}\text{[ICSE 2008]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{(i) Let the principal be Rs }P.$
$\displaystyle \text{Simple Interest}=\frac{P\times4\times2}{100}=340$
$\displaystyle \frac{8P}{100}=340$
$\displaystyle P=\frac{340\times100}{8}$
$\displaystyle =4250$
$\displaystyle \therefore \text{Sum of money}= \text{Rs }4250$
$\displaystyle \text{(ii) Rate per half-year}=2\%$
$\displaystyle \text{Compound Interest}=4250\left(1+\frac{2}{100}\right)^{2}-4250$
$\displaystyle =4250(1.02)^{2}-4250$
$\displaystyle =4421.70-4250$
$\displaystyle =171.70$
$\displaystyle \therefore \text{Compound Interest}= \text{Rs }171.70$
$\\$

$\displaystyle \textbf{Question 61. }\text{Mr. Dubey borrows Rs }100000\text{ from State Bank of India at }11\%\text{ per annum}$
$\displaystyle \text{compound interest. He repays Rs }41000\text{ at the end of first year and Rs }47700$
$\displaystyle \text{at the end of the second year. Find the amount outstanding at the}$
$\displaystyle \text{beginning of the third year.}\hspace{0.2cm}\text{[ICSE 2009]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Amount due at the end of first year}=100000\times1.11$
$\displaystyle =111000$
$\displaystyle \text{Balance after first repayment}=111000-41000$
$\displaystyle =70000$
$\displaystyle \text{Amount due at the end of second year}=70000\times1.11$
$\displaystyle =77700$
$\displaystyle \text{Balance after second repayment}=77700-47700$
$\displaystyle =30000$
$\displaystyle \therefore \text{Amount outstanding at the beginning of the third year}= \text{Rs }30000$
$\\$

$\displaystyle \textbf{Question 62. }\text{Mr. Kumar borrowed Rs }15000\text{ for two years. The rate of interest for the}$
$\displaystyle \text{two successive years are }8\%\text{ and }10\%\text{ respectively. If he repays Rs }6200\text{ at the}$
$\displaystyle \text{end of the first year, find the outstanding amount at the end of the second}$
$\displaystyle \text{year.}\hspace{0.2cm}\text{[ICSE 2011]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Amount due at the end of first year}=15000\left(1+\frac{8}{100}\right)$
$\displaystyle =16200$
$\displaystyle \text{Balance after repayment}=16200-6200$
$\displaystyle =10000$
$\displaystyle \text{Amount due at the end of second year}=10000\left(1+\frac{10}{100}\right)$
$\displaystyle =11000$
$\displaystyle \therefore \text{Outstanding amount at the end of the second year}= \text{Rs }11000$
$\\$

$\displaystyle \textbf{Question 63. }\text{Mrs. Kapoor opened a Savings Bank Account in State Bank of India on }9\text{th}$
$\displaystyle \text{January }2008.\text{ Her pass book entries for the year }2008\text{ are given below :}$

$\displaystyle \begin{array}{|c|l|c|c|c|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (in Rs.)} & \text{Deposits (in Rs.)} & \text{Balance (in Rs.)} \\ \hline \text{Jan 9, 2008} & \text{By Cash} & - & 10000 & 10000 \\ \hline \text{Feb 12, 2008} & \text{By Cash} & - & 15500 & 25500 \\ \hline \text{Apr 6, 2008} & \text{To Cheque} & 3500 & - & 22000 \\ \hline \text{Apr 30, 2008} & \text{To Self} & 2000 & - & 20000 \\ \hline \text{Jul 16, 2008} & \text{By Cheque} & - & 6500 & 26500 \\ \hline \text{Aug 4, 2008} & \text{To Self} & 5500 & - & 21000 \\ \hline \text{Aug 20, 2008} & \text{To Cheque} & 1200 & - & 19800 \\ \hline \text{Dec 12, 2008} & \text{By Cash} & - & 1700 & 21500 \\ \hline \end{array}$

$\displaystyle \text{Mrs. Kapoor closes the account on }31\text{st December, }2008.\text{ If the bank pays interest}$
$\displaystyle \text{at }4\%\text{ per annum, find the interest Mrs. Kapoor receives on closing the account.}$
$\displaystyle \text{Give your answer correct to the nearest rupee.}\hspace{0.2cm}\text{[ICSE 2010]}$

$\displaystyle \text{Answer:}$

$\displaystyle \begin{array}{|c|c|} \hline \text{Month} & \text{Minimum balance from 10th to end of month} \\ \hline \text{January} & 10000 \\ \hline \text{February} & 10000 \\ \hline \text{March} & 25500 \\ \hline \text{April} & 20000 \\ \hline \text{May} & 20000 \\ \hline \text{June} & 20000 \\ \hline \text{July} & 20000 \\ \hline \text{August} & 19800 \\ \hline \text{September} & 19800 \\ \hline \text{October} & 19800 \\ \hline \text{November} & 19800 \\ \hline \end{array}$

$\displaystyle \text{Total of minimum balances}=10000+10000+25500+20000+20000+20000$
$\displaystyle +20000+19800+19800+19800+19800$
$\displaystyle =204700$
$\displaystyle \text{Interest}=\frac{204700\times4\times1}{100\times12}$
$\displaystyle =682.33$
$\displaystyle \therefore \text{Interest received}= \text{Rs }682\text{ approximately}$
$\\$

$\displaystyle \textbf{Question 64. }\text{Mr. R. K. Nair gets Rs }6455\text{ at the end of one year at the rate of }14\%\text{ per annum}$
$\displaystyle \text{in a recurring deposit account. Find the monthly instalment.} \hspace{0.2cm}\text{[ICSE 2005]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the monthly instalment be Rs }P.$
$\displaystyle \text{Total amount deposited in }12\text{ months}=12P$
$\displaystyle \text{Interest on recurring deposit}=\frac{P\times n(n+1)}{2\times12}\times\frac{R}{100}$
$\displaystyle \text{where }n=12,\ R=14$
$\displaystyle \text{Interest}=\frac{P\times12\times13}{2\times12}\times\frac{14}{100}$
$\displaystyle =13P\times\frac{7}{100}$
$\displaystyle =0.91P$
$\displaystyle \text{Maturity value}=12P+0.91P$
$\displaystyle =12.91P$
$\displaystyle 12.91P=6455$
$\displaystyle P=\frac{6455}{12.91}$
$\displaystyle =500$
$\displaystyle \therefore \text{Monthly instalment}= \text{Rs }500$
$\\$

$\displaystyle \textbf{Question 65. }\text{Mrs. Kumar has an account with The Bank of India. The following entries are}$
$\displaystyle \text{from her pass book :}$
$\displaystyle \begin{array}{|c|c|c|c|c|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals Rs. P} & \text{Deposits Rs. P} & \text{Balance Rs. P} \\ \hline 08.02.06 & \text{B/F} & - & - & 8500.00 \\ \hline 18.02.06 & \text{To self} & 4000.00 & - & - \\ \hline 12.04.06 & \text{By cash} & - & 2238.00 & - \\ \hline 15.06.06 & \text{To self} & 5000.00 & - & - \\ \hline 08.07.06 & \text{By cash} & - & 6000.00 & - \\ \hline \end{array}$

$\displaystyle \text{Complete the above page of her pass book and calculate the interest for the six months,}$
$\displaystyle \text{February to July, }2006,\text{ at }4.5\%\text{ per annum.}\hspace{0.2cm}\text{[ICSE 2007]}$
$\displaystyle \text{Answer:}$
$\displaystyle \begin{array}{|c|c|c|c|c|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals Rs. P} & \text{Deposits Rs. P} & \text{Balance Rs. P} \\ \hline 08.02.06 & \text{B/F} & - & - & 8500.00 \\ \hline 18.02.06 & \text{To self} & 4000.00 & - & 4500.00 \\ \hline 12.04.06 & \text{By cash} & - & 2238.00 & 6738.00 \\ \hline 15.06.06 & \text{To self} & 5000.00 & - & 1738.00 \\ \hline 08.07.06 & \text{By cash} & - & 6000.00 & 7738.00 \\ \hline \end{array}$

$\displaystyle \begin{array}{|c|c|} \hline \text{Month} & \text{Minimum balance from 10th to end of month} \\ \hline \text{February} & 4500 \\ \hline \text{March} & 4500 \\ \hline \text{April} & 6738 \\ \hline \text{May} & 6738 \\ \hline \text{June} & 1738 \\ \hline \text{July} & 7738 \\ \hline \end{array}$
$\displaystyle \text{Total of minimum balances}=4500+4500+6738+6738+1738+7738$
$\displaystyle =31952$
$\displaystyle \text{Interest}=\frac{31952\times4.5\times1}{100\times12}$
$\displaystyle =119.82$
$\displaystyle \therefore \text{Interest}= \text{Rs }119.82$
$\\$

$\displaystyle \textbf{Question 66. }\text{The entries in a Savings Bank Pass Book are as given below :}$
$\displaystyle \begin{array}{|c|c|c|c|c|} \hline \text{Dates} & \text{Particulars} & \text{Withdrawal} & \text{Deposit} & \text{Balance} \\ \hline 01.01.03 & \text{B/F} & - & - & \text{Rs. }14000 \\ \hline 01.02.03 & \text{By cash} & - & \text{Rs. }11500 & \text{Rs. }25500 \\ \hline 12.02.03 & \text{To cheque} & \text{Rs. }5000 & - & \text{Rs. }20500 \\ \hline 05.04.03 & \text{To cash} & - & \text{Rs. }3750 & \text{Rs. }24250 \\ \hline 15.04.03 & \text{To cheque} & \text{Rs. }4250 & - & \text{Rs. }20000 \\ \hline 09.05.03 & \text{By cash} & - & \text{Rs. }1500 & \text{Rs. }21500 \\ \hline 04.06.03 & \text{By cash} & - & \text{Rs. }1500 & \text{Rs. }23000 \\ \hline \end{array}$
$\displaystyle \text{Calculate the interest for six months (January to June) at }4\%\text{ per annum}$
$\displaystyle \text{on the minimum balance on or after the tenth day of each month.}\hspace{0.2cm}\text{[ICSE 2004]}$
$\displaystyle \text{Answer:}$
$\displaystyle \begin{array}{|c|c|} \hline \text{Month} & \text{Minimum balance on or after 10th day} \\ \hline \text{January} & 14000 \\ \hline \text{February} & 20500 \\ \hline \text{March} & 20500 \\ \hline \text{April} & 20000 \\ \hline \text{May} & 21500 \\ \hline \text{June} & 23000 \\ \hline \end{array}$
$\displaystyle \text{Total of minimum balances}=14000+20500+20500+20000+21500+23000$
$\displaystyle =119500$
$\displaystyle \text{Interest}=\frac{119500\times4\times1}{100\times12}$
$\displaystyle =398.33$
$\displaystyle \therefore \text{Interest}= \text{Rs. }398.33$
$\\$

$\displaystyle \textbf{Question 67. }\text{Mohan deposits Rs. }80\text{ per month in a cumulative deposit account for six years.}$
$\displaystyle \text{Find the amount payable to him on maturity, if the rate of interest is }6\%\text{ per}$
$\displaystyle \text{annum.}\hspace{0.2cm}\text{[ICSE 2006]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=80,\quad n=6\times12=72,\quad R=6\%$
$\displaystyle \text{Interest}=\frac{P\times n(n+1)}{2\times12}\times\frac{R}{100}$
$\displaystyle =\frac{80\times72\times73}{2\times12}\times\frac{6}{100}$
$\displaystyle =1051.20$
$\displaystyle \text{Total deposit}=80\times72=5760$
$\displaystyle \text{Maturity value}=5760+1051.20$
$\displaystyle =6811.20$
$\displaystyle \therefore \text{Amount payable on maturity}= \text{Rs. }6811.20$
$\\$

$\displaystyle \textbf{Question 68. }\text{Saloni deposited Rs. }150\text{ per month in her bank for eight months under the}$
$\displaystyle \text{Recurring Deposit Scheme. What will be the maturity value of her deposit, if}$
$\displaystyle \text{the rate of interest is }8\%\text{ per annum and the interest is calculated at the end of}$
$\displaystyle \text{every month ?}\hspace{0.2cm}\text{[ICSE 2007]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=150,\quad n=8,\quad R=8\%$
$\displaystyle \text{Interest}=\frac{P\times n(n+1)}{2\times12}\times\frac{R}{100}$
$\displaystyle =\frac{150\times8\times9}{2\times12}\times\frac{8}{100}$
$\displaystyle =36$
$\displaystyle \text{Total deposit}=150\times8=1200$
$\displaystyle \text{Maturity value}=1200+36$
$\displaystyle =1236$
$\displaystyle \therefore \text{Maturity value}= \text{Rs. }1236$
$\\$