Class 10: Banking – Exercise 4(c)

$\displaystyle \textbf{Question 1: }\text{Given below are the entries in a Saving Bank A/C passbook:}$
$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{Feb. 8} & \text{B/F} & - & - & 8500\\ \text{Feb. 18} & \text{To Self} & 4000 & - & 4500\\ \text{April 12} & \text{By Cash} & - & 2230 & 6730\\ \text{June 15} & \text{To Self} & 5000 & - & 1730\\ \text{July 8} & \text{By Cash} & - & 6000 & 7730\\ \hline \end{array}$
$\displaystyle \text{Calculate the interest for six months from February to July at }6\%\text{ p.a.} \hfill \text{[ICSE 2013]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}$
$\displaystyle \text{day of each month.}$
$\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{February} & 4500\\ \text{March} & 4500\\ \text{April} & 4500\\ \text{May} & 6730\\ \text{June} & 1730\\ \text{July} & 7730\\ \hline \text{Total} & 29690\\ \hline \end{array}$
$\displaystyle P=\text{Rs. }29690,\ R=6\%\text{ and }T=\frac{1}{12}\text{ year}$
$\displaystyle I=P\times R\times T$
$\displaystyle I=29690\times\frac{6}{100}\times\frac{1}{12}$
$\displaystyle I=\text{Rs. }148.45$
$\displaystyle \therefore \text{Interest for six months}=\text{Rs. }148.45$
$\\$

$\displaystyle \textbf{Question 2: }\text{A page from the passbook of a Saving Bank Account is given below:}$
$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline 09.08.1999 & \text{By Cash} & - & 10000 & 10000\\ 11.08.1999 & \text{By Cheque} & - & 5000 & 15000\\ 05.10.1999 & \text{To Cheque} & 12000 & - & 3000\\ 10.10.1999 & \text{By Cash} & - & 17000 & 20000\\ 27.11.1999 & \text{To Cheque} & 5000 & - & 15000\\ 29.11.1999 & \text{By Cash} & - & 3000 & 18000\\ \hline \end{array}$
$\displaystyle \text{The account is closed on }2^{\text{nd}}\text{ January 2000. Find the amount received,}$
$\displaystyle \text{if the rate of interest is }5\%\text{ per annum.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}\text{ day of each month.}$
$\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{August} & 10000\\ \text{September} & 15000\\ \text{October} & 20000\\ \text{November} & 15000\\ \text{December} & 18000\\ \text{January} & 0\\ \hline \text{Total} & 78000\\ \hline \end{array}$
$\displaystyle P=\text{Rs. }78000,\ R=5\%\text{ and }T=\frac{1}{12}\text{ year}$
$\displaystyle I=P\times R\times T$
$\displaystyle I=78000\times\frac{5}{100}\times\frac{1}{12}=\text{Rs. }325$
$\displaystyle \text{Amount received}=18000+325=\text{Rs. }18325$
$\\$

$\displaystyle \textbf{Question 3: }\text{A person had an account in a bank. His passbook had the following}$
$\displaystyle \text{entries:}$
$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{Jan. 1, 2000} & \text{By Balance} & - & - & 9600\\ \text{Jan. 8} & \text{By Cash} & - & 6000 & 15600\\ \text{Feb. 18} & \text{To Cheque} & 10500 & - & 5100\\ \text{May 19} & \text{By Cash} & - & 6300 & 11400\\ \text{July 15} & \text{By Self} & 2400 & - & 9000\\ \text{Oct. 7} & \text{By Cash} & - & 3600 & 12000\\ \hline \end{array}$
$\displaystyle \text{On }30^{\text{th}}\text{ October 2000, he closed the account. If the interest received}$
$\displaystyle \text{on closing the account was Rs. }310,\text{ calculate the rate of interest per annum.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}\text{ day of each month.}$
$\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{January} & 15600\\ \text{February} & 5100\\ \text{March} & 5100\\ \text{April} & 5100\\ \text{May} & 5100\\ \text{June} & 11400\\ \text{July} & 9000\\ \text{August} & 9000\\ \text{September} & 9000\\ \text{October} & 12000\\ \hline \text{Total} & 86400\\ \hline \end{array}$
$\displaystyle P=\text{Rs. }86400,\ R=r\%,\ T=\frac{1}{12}\text{ year and }I=\text{Rs. }310$
$\displaystyle I=P\times\frac{R}{100}\times T$
$\displaystyle 310=86400\times\frac{r}{100}\times\frac{1}{12}$
$\displaystyle r=\frac{310\times1200}{86400}=4.31\%$
$\displaystyle \therefore \text{The rate of interest is }4.31\%\text{ per annum.}$
$\\$

$\displaystyle \textbf{Question 4: }\text{A person deposited Rs. }600\text{ per month in a Recurring Deposit}$
$\displaystyle \text{Account for }4\text{ years. If the rate of interest is }8\%\text{ per annum,}$
$\displaystyle \text{calculate the maturity value of the account.}$
$\displaystyle \text{Answer:}$
$\displaystyle P=\text{Rs. }600,\ n=48,\ r=8\%$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle =600\times48+600\times\frac{48(48+1)}{2\times12}\times\frac{8}{100}$
$\displaystyle =28800+4704=\text{Rs. }33504$
$\\$

$\displaystyle \textbf{Question 5: }\text{A person has a Recurring Deposit Account in a bank and deposits}$
$\displaystyle \text{Rs. }80\text{ per month for }18\text{ months. Find the rate of interest paid by}$
$\displaystyle \text{the bank if the maturity value of the account is Rs. }1554.$
$\displaystyle \text{Answer:}$
$\displaystyle P=\text{Rs. }80,\ n=18,\ r=r\%,\ \text{Maturity Value}=\text{Rs. }1554$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 1554=80\times18+80\times\frac{18(18+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle r=\frac{(1554-80\times18)\times(2\times12)\times100}{80\times18\times19}$
$\displaystyle r=10\%$
$\displaystyle \therefore \text{The rate of interest is }10\%\text{ per annum.}$
$\\$

$\displaystyle \textbf{Question 6: }\text{The maturity value of a Recurring Deposit Account is Rs. }16176.$
$\displaystyle \text{If the monthly installment is Rs. }400\text{ and the rate of interest is }8\%,$
$\displaystyle \text{find the time of this account.}$
$\displaystyle \text{Answer:}$
$\displaystyle P=\text{Rs. }400,\ n=n,\ r=8\%,\ \text{Maturity Value}=\text{Rs. }16176$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 16176=400n+400\times\frac{n(n+1)}{2\times12}\times\frac{8}{100}$
$\displaystyle 16176=400n+\frac{4}{3}n(n+1)$
$\displaystyle 48528=1200n+4n(n+1)$
$\displaystyle n^2+301n-12132=0$
$\displaystyle (n-36)(n+337)=0$
$\displaystyle n=36\text{ or }n=-337$
$\displaystyle \text{Since the number of months cannot be negative, }n=36.$
$\displaystyle \therefore \text{The time of the account is }36\text{ months, i.e., }3\text{ years.}$
$\\$

$\displaystyle \textbf{Question 7: }\text{A person needs Rs. }30000\text{ after }2\text{ years. What least money}$
$\displaystyle \text{in multiple of Rs. }5\text{ must he deposit every month in a Recurring Deposit}$
$\displaystyle \text{Account to get the required money after }2\text{ years, the rate of interest}$
$\displaystyle \text{being }8\%\text{ per annum?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the monthly deposit be Rs. }x.$
$\displaystyle P=\text{Rs. }x,\ n=24,\ r=8\%,\ \text{Maturity Value}=\text{Rs. }30000$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 30000=24x+x\times\frac{24(24+1)}{2\times12}\times\frac{8}{100}$
$\displaystyle 30000=24x+2x$
$\displaystyle 30000=26x$
$\displaystyle x=\frac{30000}{26}=\text{Rs. }1153.84$
$\displaystyle \text{The least multiple of Rs. }5\text{ greater than Rs. }1153.84\text{ is Rs. }1155.$
$\displaystyle \therefore \text{He must deposit Rs. }1155\text{ every month.}$
$\\$

$\displaystyle \textbf{Question 8: }\text{A person has a Recurring Deposit Account in a bank for }3\text{ years}$
$\displaystyle \text{at }8\%\text{ per annum simple interest. If he gets Rs. }9990\text{ as interest}$
$\displaystyle \text{at the time of maturity, find:}$
$\displaystyle \text{(i) The monthly installment}\qquad\text{(ii) The maturity amount}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the monthly installment be Rs. }x.$
$\displaystyle n=36,\ r=8\%,\ I=\text{Rs. }9990$
$\displaystyle I=P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 9990=x\times\frac{36(36+1)}{2\times12}\times\frac{8}{100}$
$\displaystyle 9990=x\times\frac{36\times37}{24}\times\frac{8}{100}$
$\displaystyle 9990=4.44x$
$\displaystyle x=\frac{9990}{4.44}=\text{Rs. }2250$
$\displaystyle \therefore \text{The monthly installment is Rs. }2250.$
$\displaystyle \text{Total amount deposited}=2250\times36=\text{Rs. }81000$
$\displaystyle \text{Maturity amount}=81000+9990=\text{Rs. }90990$
$\displaystyle \therefore \text{The maturity amount is Rs. }90990.$
$\\$

$\displaystyle \textbf{Question 9: }\text{A person has a cumulative Recurring Deposit Account and deposits}$
$\displaystyle \text{Rs. }900\text{ per month for }4\text{ years. If he gets Rs. }52020\text{ at the time}$
$\displaystyle \text{of maturity, find the rate of interest.}$
$\displaystyle \text{Answer:}$
$\displaystyle P=\text{Rs. }900,\ n=48,\ r=r\%,\ \text{Maturity Value}=\text{Rs. }52020$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 52020=900\times48+900\times\frac{48(48+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle r=\frac{(52020-900\times48)\times(2\times12)\times100}{900\times48\times49}$
$\displaystyle r=10\%$
$\displaystyle \therefore \text{The rate of interest is }10\%\text{ per annum.}$
$\\$

$\displaystyle \textbf{Question 10: }\text{A person has a }4\text{-year Recurring Deposit Account in a bank}$
$\displaystyle \text{and deposits Rs. }1800\text{ per month. If she gets Rs. }108450\text{ at the}$
$\displaystyle \text{time of maturity, find the rate of interest.}$
$\displaystyle \text{Answer:}$
$\displaystyle P=\text{Rs. }1800,\ n=48,\ r=r\%,\ \text{Maturity Value}=\text{Rs. }108450$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 108450=1800\times48+1800\times\frac{48(48+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle r=\frac{(108450-1800\times48)\times(2\times12)\times100}{1800\times48\times49}$
$\displaystyle r=12.5\%$
$\displaystyle \therefore \text{The rate of interest is }12.5\%\text{ per annum.}$
$\\$

$\displaystyle \textbf{Question 11: }\text{Chaudhary opened a Saving Bank Account at State Bank of India}$
$\displaystyle \text{on }1^{\text{st}}\text{ April 2007. The entries of one year as shown in his passbook}$
$\displaystyle \text{are given below:}\hfill \text{[ICSE 2011]}$
$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline 1^{\text{st}}\text{ April 2007} & \text{By Cash} & - & 8550 & 8550\\ 12^{\text{th}}\text{ April 2007} & \text{To Self} & 1200 & - & 7350\\ 24^{\text{th}}\text{ April 2007} & \text{By Cash} & - & 4550 & 11900\\ 8^{\text{th}}\text{ July 2007} & \text{By Cheque} & - & 1500 & 13400\\ 10^{\text{th}}\text{ Sept. 2007} & \text{By Cheque} & - & 3500 & 16900\\ 17^{\text{th}}\text{ Sept. 2007} & \text{To Cheque} & 2500 & - & 14400\\ 11^{\text{th}}\text{ Oct. 2007} & \text{By Cash} & - & 800 & 15200\\ 6^{\text{th}}\text{ Jan. 2008} & \text{To Self} & 2000 & - & 13200\\ 9^{\text{th}}\text{ March 2008} & \text{By Cheque} & - & 950 & 14150\\ \hline \end{array}$
$\displaystyle \text{If the bank pays interest at }5\%\text{ per annum, find the interest paid}$
$\displaystyle \text{on }1^{\text{st}}\text{ April 2008. Give your answer correct to the nearest rupee.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}\text{ day of each month.}$
$\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{April} & 7350\\ \text{May} & 11900\\ \text{June} & 11900\\ \text{July} & 13400\\ \text{August} & 13400\\ \text{September} & 14400\\ \text{October} & 14400\\ \text{November} & 15200\\ \text{December} & 15200\\ \text{January} & 13200\\ \text{February} & 13200\\ \text{March} & 14150\\ \hline \text{Total} & 157700\\ \hline \end{array}$
$\displaystyle P=\text{Rs. }157700,\ R=5\%\text{ and }T=\frac{1}{12}\text{ year}$
$\displaystyle I=P\times R\times T$
$\displaystyle I=157700\times\frac{5}{100}\times\frac{1}{12}$
$\displaystyle I=\text{Rs. }657.08$
$\displaystyle \therefore \text{Interest paid}=\text{Rs. }657\text{, correct to the nearest rupee.}$
$\\$

$\displaystyle \textbf{Question 12: }\text{Bitto deposits a certain sum of money in a Recurring Deposit}$
$\displaystyle \text{Account of a bank. If the rate of interest is }8\%\text{ per annum and}$
$\displaystyle \text{he gets Rs. }8008\text{ after }3\text{ years, find the monthly installment.} \hfill \text{[ICSE 2013]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the monthly installment be Rs. }x.$
$\displaystyle P=\text{Rs. }x,\ n=36,\ r=8\%,\ \text{Maturity Value}=\text{Rs. }8008$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 8008=36x+x\times\frac{36(36+1)}{2\times12}\times\frac{8}{100}$
$\displaystyle 8008=40.44x$
$\displaystyle x=\frac{8008}{40.44}=\text{Rs. }198.02$
$\displaystyle \therefore \text{He must deposit Rs. }200\text{ every month.}$
$\\$

$\displaystyle \textbf{Question 13: }\text{Shahrukh opened a Recurring Deposit Account in a bank and}$
$\displaystyle \text{deposited Rs. }800\text{ per month for }1\frac{1}{2}\text{ years. If he received}$
$\displaystyle \text{Rs. }15084\text{ at the time of maturity, find the rate of interest per annum.} \hfill \text{[ICSE 2014]}$
$\displaystyle \text{Answer:}$
$\displaystyle P=\text{Rs. }800,\ n=18,\ r=r\%,\ \text{Maturity Value}=\text{Rs. }15084$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle 15084=800\times18+800\times\frac{18(18+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle r=\frac{(15084-800\times18)\times(2\times12)\times100}{800\times18\times19}$
$\displaystyle r=6\%$
$\displaystyle \therefore \text{The rate of interest is }6\%\text{ per annum.}$
$\\$

$\displaystyle \textbf{Question 14: }\text{A page from the Saving Bank Account of Priyanka is given below:}$
$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline 03/04/2006 & \text{B/F} & - & - & 4000\\ 05/04/2006 & \text{By Cash} & - & 2000 & 6000\\ 18/04/2006 & \text{By Cheque} & - & 6000 & 12000\\ 25/05/2006 & \text{To Cheque} & 5000 & - & 7000\\ 30/05/2006 & \text{By Cash} & - & 3000 & 10000\\ 20/07/2006 & \text{By Self} & 4000 & - & 6000\\ 10/09/2006 & \text{By Cash} & - & 2000 & 8000\\ 19/09/2006 & \text{To Cheque} & 1000 & - & 7000\\ \hline \end{array}$
$\displaystyle \text{If the interest earned by Priyanka for the period ending September 2006}$
$\displaystyle \text{is Rs. }175,\text{ find the rate of interest.}\hfill \text{[ICSE 2014]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}\text{ day of each month.}$
$\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{April} & 6000\\ \text{May} & 7000\\ \text{June} & 10000\\ \text{July} & 6000\\ \text{August} & 6000\\ \text{September} & 7000\\ \hline \text{Total} & 42000\\ \hline \end{array}$
$\displaystyle P=\text{Rs. }42000,\ R=r\%,\ T=\frac{1}{12}\text{ year and }I=\text{Rs. }175$
$\displaystyle I=P\times\frac{R}{100}\times T$
$\displaystyle 175=42000\times\frac{r}{100}\times\frac{1}{12}$
$\displaystyle r=\frac{175\times1200}{42000}=5\%$
$\displaystyle \therefore \text{The rate of interest is }5\%\text{ per annum.}$
$\\$