Question 1: Ronit opened a savings bank account with a bank on 16th May, 1997 and deposited Rs. 850. He withdrew Rs. 300 on 3rd June, 1997 and after that he neither deposited nor withdrew any money during June 1997. What is the amount on which he would receive the interest of: (i) May 1997? (ii) June 1997?
\displaystyle \text{Answer:}
\displaystyle \text{(i) Amount for May 1997 } = \text{Rs. } 0
\displaystyle \text{Reason: Account opened after 10th, so no interest for May.}
\displaystyle \text{(ii) Amount for June 1997 } = \text{Rs. } 550
\displaystyle \text{Reason: Balance up to 3rd June } = 850
\displaystyle \text{Withdrawal on 3rd June } = 300
\displaystyle \text{Minimum balance after 10th June } = 850 - 300 = 550
\\
Question 2: Mr. Sharma has a savings bank account with Bank of Baroda. A part of the page of his pass-book is shown below:
\begin{array} {|l |l |r |r |r | } \hline \text{Date} & \text{Particulars} & \text{Amount } & \text{Amount } & \text{Balance (Rs.)} \\ & &\text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \\ \hline \text{July 1, 98} & \text{B/F } & & & 1500.00 \\ \hline \text{July 8, 98} & \text{By Cheque} & & 1200.00 & 2700.00 \\ \hline \text{July 23, 98} & \text{By Cash} & & 800.00 & 3500.00 \\ \hline \text{Aug. 17, 98} & \text{By Cheque} &1600.00 & & 1900.00 \\ \hline \text{Aug. 27, 98} & \text{By Cash} & & 600.00 & 2500.00 \\ \hline \end{array}
\displaystyle \text{Answer:}
\displaystyle \text{July: Minimum balance after 10th } = \text{Rs. } 2700
\displaystyle \text{August: Minimum balance after 10th } = \text{Rs. } 1900
\\
Question 3: Mr. Dhoni has an account in the Union Bank of India. The following entries are from his passbook:
\begin{array} {|l |l |r |r |r | } \hline \text{Date} & \text{Particulars} & \text{Amount } & \text{Amount } & \text{Balance (Rs.)} \\ & &\text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \\ \hline \text{Jan 3, 07} & \text{B/F } & & & 2642.00 \\ \hline \text{Jan 16} & \text{To Self} & 640.00 & & 2002.00 \\ \hline \text{March 5} & \text{By Cash} & & 850.00 & 2852.00 \\ \hline \text{April 10} & \text{To Self} & 1130.00 & & 1722.00 \\ \hline \text{April 25} & \text{By Cheque} & & 650.00 & 2372.00 \\ \hline \text{June 15} & \text{By Cash} & 577.00 & & 1795.00 \\ \hline \end{array}
Calculate the interest from January 2007 to June 2007 at the rate of 4% per annum.       [ICSE Board 2008]
\displaystyle \text{Answer:}
\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,\hspace{0.5cm} R=4\%,\hspace{0.5cm} T=\frac{1}{12}\text{ year}
\displaystyle \text{Interest}=\frac{P \times R \times T}{100}=\frac{12745 \times 4 \times 1}{100 \times 12}=\text{Rs. }42.48
\\
Question 4: Divya opened a savings bank account in a bank on 18th October. Her passbook has the following entries:
\begin{array} {|l |l |r |r |r | } \hline \text{Date} & \text{Particulars} & \text{Amount } & \text{Amount } & \text{Balance (Rs.)} \\ & &\text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \\ \hline \text{Oct. 18} & \text{By Cash} & & 700.00 & 700.00 \\ \hline \text{Oct. 25} & \text{By Cheque} & & 800.00 & 1500.00 \\ \hline \text{Nov. 5} & \text{By Cheque} & 300.00 & & 1200.00 \\ \hline \text{Nov. 10} & \text{By Cash} & & 1300.00 & 2500.00 \\ \hline \text{Nov. 18} & \text{By Cash} & 900.00 & & 1600.00 \\ \hline \text{Dec. 3} & \text{By Cash} & 400.00 & & 1200.00 \\ \hline \text{Dec. 21} & \text{By Cheque} & & 1500.00 & 2700.00 \\ \hline \text{Jan. 5} & \text{By Cash} & & 300.00 & 3000.00 \\ \hline \end{array}
Divya closes the account on 18th January. Calculate the interest earned by her at 5% per annum.
\displaystyle \text{Answer:}
\displaystyle \text{Principal for October}=\text{Rs. }0.00
\displaystyle \text{Principal for November}=\text{Rs. }1600.00
\displaystyle \text{Principal for December}=\text{Rs. }1200.00
\displaystyle \text{Total principal}=1600.00+1200.00=\text{Rs. }2800.00
\displaystyle \text{No interest for January since the account was closed on 18th January.}
\displaystyle P=\text{Rs. }2800,\hspace{0.5cm} R=5\%,\hspace{0.5cm} T=\frac{1}{12}\text{ year}
\displaystyle \text{Interest}=\frac{P \times R \times T}{100}=\frac{2800 \times 5 \times 1}{100 \times 12}=\text{Rs. }11.67
\\
Question 5: Given below are the entries in a savings bank passbook:
\begin{array} {|l |l |r |r |r | } \hline \text{Date} & \text{Particulars} & \text{Amount } & \text{Amount } & \text{Balance (Rs.)} \\ & &\text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \\ \hline \text{February 8} & \text{B/F} & & & 8500 \\ \hline \text{February 18} & \text{To Self} & 4000 & & \\ \hline \text{April 12} & \text{By Cash} & & 2238 & \\ \hline \text{June 15} & \text{To Self} & 5000 & & \\ \hline \text{July 8} & \text{By Cash} & & 6000 & \\ \hline \end{array}
Calculate the interest for the six months, February to July, at \displaystyle 4 \frac{1}{2}\% p.a. on the minimum balance on or after the 10th day of each month.       [ICSE Board 2000, 2007]
\displaystyle \text{Answer:}
\begin{array} {|l |l |r |r |r | } \hline \text{Date} & \text{Particulars} & \text{Amount } & \text{Amount } & \text{Balance (Rs.)} \\ & &\text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \\ \hline \text{February 8} & \text{B/F} & & & 8500 \\ \hline \text{February 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{July 8} & \text{By Cash} & & 6000 & 7738 \\ \hline \end{array}
\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,\hspace{0.5cm} R=4\frac{1}{2}\%,\hspace{0.5cm} T=\frac{1}{12}\text{ year}
\displaystyle \text{Interest}=\frac{29714 \times 9 \times 1}{100 \times 2 \times 12}=\text{Rs. }111.43
\begin{array}{|l|c|c|} \hline \text{Month} & \text{Principal (Rs.)} & \text{Rounded (Rs.)} \\ \hline \text{February} & 4500 & 4500 \\ \hline \text{March} & 4500 & 4500 \\ \hline \text{April} & 4500 & 4500 \\ \hline \text{May} & 6738 & 6740 \\ \hline \text{June} & 1738 & 1740 \\ \hline \text{July} & 7738 & 7740 \\ \hline \text{Total} & 29714 & 29720 \\ \hline \end{array}
\displaystyle P=\text{Rs. }29720,\hspace{0.5cm} R=4\frac{1}{2}\%,\hspace{0.5cm} T=\frac{1}{12}\text{ year}
\displaystyle \text{Interest}=\frac{29720 \times 9 \times 1}{100 \times 2 \times 12}=\text{Rs. }111.45
\\
Question 6: Mr. Shiv Kumar has a Savings Bank Account in the Punjab National Bank. His passbook has the following entries:
\begin{array} {|l |l |r |r |r | } \hline \text{Date} & \text{Particulars} & \text{Amount } & \text{Amount } & \text{Balance (Rs.)} \\ & &\text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \\ \hline \text{April 1, 1998} & \text{B/F} & & & 3220.00 \\ \hline \text{April 15} & \text{By Transfer} & & 2010.00 & 5230.00 \\ \hline \text{May 8} & \text{To Cheque No.355} & 298.00 & & 4932.00 \\ \hline \text{July 15} & \text{By Clearing} & & 4628.00 & 9560.00 \\ \hline \text{July 29} & \text{By Cash} & & 5440.00 & 15000.00 \\ \hline \text{September 10} & \text{To Self} & 6980.00 & & 8020.00 \\ \hline \text{January 10, 1999} & \text{By Cash} & & 8000.00 & 16020.00 \\ \hline \end{array}
Calculate the interest due to him at the end of the financial year (March 31, 1999) at the rate of 6% per annum. [ICSE Board 2002]
\displaystyle \text{Answer:}
\begin{array}{|l|c|c|} \hline \text{Month} & \text{Principal (Rs.)} & \text{Rounded (Rs.)} \\ \hline \text{April} & 3220 & 3220 \\ \hline \text{May} & 4932 & 4930 \\ \hline \text{June} & 4932 & 4930 \\ \hline \text{July} & 4932 & 4930 \\ \hline \text{August} & 15000 & 15000 \\ \hline \text{September} & 8020 & 8020 \\ \hline \text{October} & 8020 & 8020 \\ \hline \text{November} & 8020 & 8020 \\ \hline \text{December} & 8020 & 8020 \\ \hline \text{January} & 16020 & 16020 \\ \hline \text{February} & 16020 & 16020 \\ \hline \text{March} & 16020 & 16020 \\ \hline \text{Total} & 113156 & 113150 \\ \hline \end{array}
\displaystyle P=\text{Rs. }113156,\hspace{0.5cm} R=6\%,\hspace{0.5cm} T=\frac{1}{12}\text{ year}
\displaystyle \text{Interest}=\frac{113156 \times 6 \times 1}{100 \times 12}=\text{Rs. }565.78
\displaystyle P=\text{Rs. }113150,\hspace{0.5cm} R=6\%,\hspace{0.5cm} T=\frac{1}{12}\text{ year}
\displaystyle \text{Interest}=\frac{113150 \times 6 \times 1}{100 \times 12}=\text{Rs. }565.75
\\
Question 7: Given the following details, calculate simple interest at the rate of 6% per annum up to June 30.       [ICSE Board 2003]
\begin{array} {|l |l |r |r | } \hline \text{Date} & \text{Debit Rs.} & \text{Credit Rs.} & \text{Balance} \\ \hline \text{January 1} & & 24000.00 & 24000.00 \\ \hline \text{January 20} & 5000.00 & & 19000.00 \\ \hline \text{January 29} & & 10000.00 & 29000.00 \\ \hline \text{March 15} & & 8000.00 & 37000.00 \\ \hline \text{April 3} & & 7653.00 & 44653.00 \\ \hline \text{May 6} & 3040.00 & & 41613.00 \\ \hline \text{May 8} & & 5087.00 & 46700.00 \\ \hline \end{array}
\displaystyle \text{Answer:}
\begin{array}{|l|c|c|} \hline \text{Month} & \text{Principal (Rs.)} & \text{Rounded (Rs.)} \\ \hline \text{January} & 19000.00 & 19000.00 \\ \hline \text{February} & 29000.00 & 29000.00 \\ \hline \text{March} & 29000.00 & 29000.00 \\ \hline \text{April} & 44653.00 & 44650.00 \\ \hline \text{May} & 46700.00 & 46700.00 \\ \hline \text{June} & 46700.00 & 46700.00 \\ \hline \text{Total} & 215053.00 & 215050.00 \\ \hline \end{array}
\displaystyle P=\text{Rs. }215053,\hspace{0.5cm} R=6\%,\hspace{0.5cm} T=\frac{1}{12}\text{ year}
\displaystyle \text{Interest}=\frac{215053 \times 6 \times 1}{100 \times 12}=\text{Rs. }1075.27
\displaystyle P=\text{Rs. }215050,\hspace{0.5cm} R=6\%,\hspace{0.5cm} T=\frac{1}{12}\text{ year}
\displaystyle \text{Interest}=\frac{215050 \times 6 \times 1}{100 \times 12}=\text{Rs. }1075.25
\\
Question 8: If the account in Question 7 was closed on June 30, calculate the interest.
\displaystyle \text{Answer:}
\begin{array}{|l|c|c|} \hline \text{Month} & \text{Principal (Rs.)} & \text{Rounded (Rs.)} \\ \hline \text{January} & 19000.00 & 19000.00 \\ \hline \text{February} & 29000.00 & 29000.00 \\ \hline \text{March} & 29000.00 & 29000.00 \\ \hline \text{April} & 44653.00 & 44650.00 \\ \hline \text{May} & 46700.00 & 46700.00 \\ \hline \text{June} & 0.00 & 0.00 \\ \hline \text{Total} & 168353.00 & 168350.00 \\ \hline \end{array}
\displaystyle P=\text{Rs. }168353,\hspace{0.5cm} R=6\%,\hspace{0.5cm} T=\frac{1}{12}\text{ year}
\displaystyle \text{Interest}=\frac{168353 \times 6 \times 1}{100 \times 12}=\text{Rs. }841.77
\displaystyle P=\text{Rs. }168350,\hspace{0.5cm} R=6\%,\hspace{0.5cm} T=\frac{1}{12}\text{ year}
\displaystyle \text{Interest}=\frac{168350 \times 6 \times 1}{100 \times 12}=\text{Rs. }841.75
\\
Question 9: The following table shows a page from the passbook of a bank:
\begin{array} {|l |l |r |r |r | } \hline \text{Date} & \text{Particulars} & \text{Amount} & \text{Amount} & \text{Balance (Rs.)} \\ & &\text{Withdrawn} & \text{Deposited} & \\ \hline \text{January 1, 03} & \text{B/F} & & & 2842.00 \\ \hline \text{January 15} & \text{To Self} & 840.00 & & 2002.00 \\ \hline \text{March 6} & \text{By Cash} & & 856.00 & 2858.00 \\ \hline \text{April 10} & \text{To Self} & 1132.00 & & 1726.00 \\ \hline \text{April 25} & \text{By Cheque} & & 638.00 & 2364.00 \\ \hline \text{June 15} & \text{By Cash} & 568.50 & & 1795.50 \\ \hline \end{array}
Calculate interest from January 2003 to June 2003 at 6% per annum. For every month take the minimum balance in the nearest multiple of Rs. 10 after 10th day.
\displaystyle \text{Answer:}
\begin{array}{|l|c|c|} \hline \text{Month} & \text{Principal (Rs.)} & \text{Rounded (Rs.)} \\ \hline \text{January} & 2002.00 & 2000.00 \\ \hline \text{February} & 2002.00 & 2000.00 \\ \hline \text{March} & 2858.00 & 2860.00 \\ \hline \text{April} & 1726.00 & 1730.00 \\ \hline \text{May} & 2364.00 & 2360.00 \\ \hline \text{June} & 1795.50 & 1800.00 \\ \hline \text{Total} & 12747.50 & 12750.00 \\ \hline \end{array}
\displaystyle P=\text{Rs. }12750,\hspace{0.5cm} R=6\%,\hspace{0.5cm} T=\frac{1}{12}\text{ year}
\displaystyle \text{Interest}=\frac{12750 \times 6 \times 1}{100 \times 12}=\text{Rs. }63.75
\\
Question 10: Mr. Ashok has an account in the Central Bank of India. The following entries are from his passbook:       [ICSE Board 2006]
\begin{array} {|l |l |r |r |r | } \hline \text{Date} & \text{Particulars} & \text{Amount } & \text{Amount } & \text{Balance (Rs.)} \\ & &\text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \\ \hline \text{01.01.05 } & \text{B/F } & & & 2842.00 \\ \hline \text{07.01.05 } & \text{By Cash} & 840.00 & & 2002.00 \\ \hline \text{17.01.05 } & \text{By Cheque} & & 856.00 & 2858.00 \\ \hline \text{10.02.05 } & \text{By Cash} & 1132.00 & & 1726.00 \\ \hline \text{25.02.05 } & \text{By Cheque} & & 638.00 & 2364.00 \\ \hline \text{20.09.05 } & \text{By Cash} & 1132.00 & & 1726.00 \\ \hline \text{11.11.05 } & \text{By Cheque} & & 638.00 & 2364.00 \\ \hline \text{05.12.05 } & \text{By Cash} & 568.50 & & 1795.50 \\ \hline \end{array}
If Mr. Ashok gets Rs. 83.75 as interest at the end of the year, where the interest is compounded annually, calculate the rate of interest paid by the bank in his Savings Bank Account on 31st December, 2005.
\displaystyle \text{Answer:}
\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,\hspace{0.5cm} I=\text{Rs. }83.75,\hspace{0.5cm} T=\frac{1}{12}\text{ year}
\displaystyle \text{Rate}=\frac{I \times 100}{P \times T}=\frac{83.75 \times 100 \times 12}{20100}=5\%
\\
Question 11: Kiran deposited Rs. 200 per month for 36 months in a bank’s recurring deposit account. If the bank pays interest at the rate of 11% per annum, find the amount she gets on maturity.       [ICSE Board 2012]
\displaystyle \text{Answer:}
\displaystyle P=\text{Rs. }200,\hspace{0.5cm} r=11\%,\hspace{0.5cm} n=36\text{ months}
\displaystyle \text{Interest}=P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}=200 \times \frac{36(36+1)}{2 \times 12} \times \frac{11}{100}=1221
\displaystyle \text{Sum deposited}=P \times n=200 \times 36=\text{Rs. }7200
\displaystyle \text{Maturity amount}=7200+1221=\text{Rs. }8421
\\
Question 12: Mohan deposited Rs. 80 per month in a cumulative deposit account for six years. Find the amount payable to him on maturity, if the rate of interest is 6% per annum.       [ICSE Board 2006]
\displaystyle \text{Answer:}
\displaystyle P=\text{Rs. }80,\hspace{0.5cm} r=6\%,\hspace{0.5cm} n=72\text{ months}
\displaystyle \text{Interest}=P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}=80 \times \frac{72(72+1)}{2 \times 12} \times \frac{6}{100}=1051.20
\displaystyle \text{Sum deposited}=P \times n=80 \times 72=\text{Rs. }5760
\displaystyle \text{Maturity amount}=5760+1051.20=\text{Rs. }6811.20
\\
Question 13: Mr. R.K. Nair gets Rs. 6455 at the end of one year at the rate of 14% per annum in a Recurring Deposit Account. Find the monthly instalment.       [ICSE Board 2005]
\displaystyle \text{Answer:}
\displaystyle \text{Let } P=\text{Rs. }x,\hspace{0.5cm} r=14\%,\hspace{0.5cm} n=12\text{ months}
\displaystyle \text{Interest}=P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}=x \times \frac{12(12+1)}{2 \times 12} \times \frac{14}{100}=0.91x
\displaystyle \text{Sum deposited}=P \times n=12x
\displaystyle \text{Maturity value}=12x+0.91x=12.91x
\displaystyle 12.91x=6455 \Rightarrow x=\frac{6455}{12.91}=\text{Rs. }500
\displaystyle \text{Monthly instalment}=\text{Rs. }500
\\
Question 14: Ahmed has a recurring deposit account in a bank. He deposits Rs. 2500 per month for 2 years. If he gets Rs. 66250 at the time of maturity, find: (i) the interest paid by the bank (ii) the rate of interest       [ICSE Board 2011]
\displaystyle \text{Answer:}
\displaystyle \text{(i) } n=24\text{ months}
\displaystyle \text{Total deposited}=24 \times 2500=\text{Rs. }60000
\displaystyle \text{Interest}=66250-60000=\text{Rs. }6250
\displaystyle \text{(ii) } P=\text{Rs. }2500,\hspace{0.5cm} I=6250,\hspace{0.5cm} n=24\text{ months}
\displaystyle 2500 \times \frac{24(24+1)}{2 \times 12} \times \frac{r}{100}=6250
\displaystyle \Rightarrow r=\frac{6250 \times 24 \times 100}{2500 \times 24 \times 25}=10\%
\\
Question 15: Monica has a C.D. Account in the Union Bank of India and deposited Rs. 600 per month. If the maturity value of this account is Rs. 24930 and the rate of interest is 10% per annum, find the time (in years) for which the account was held.
\displaystyle \text{Answer:}
\displaystyle \text{Let the account be held for } n \text{ months}
\displaystyle P=\text{Rs. }600,\hspace{0.5cm} r=10\%
\displaystyle \text{Interest}=P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}=600 \times \frac{n(n+1)}{2 \times 12} \times \frac{10}{100}=\frac{5n(n+1)}{2}
\displaystyle 600n+\frac{5n(n+1)}{2}=24930
\displaystyle \Rightarrow 5n^2+1205n-49860=0
\displaystyle \Rightarrow n^2+241n-9972=0
\displaystyle \Rightarrow n^2+277n-36n-9972=0
\displaystyle \Rightarrow n(n+277)-36(n+277)=0
\displaystyle \Rightarrow (n+277)(n-36)=0
\displaystyle \Rightarrow n=-277 \text{ or } n=36
\displaystyle \text{Since } n \text{ cannot be negative, } n=36
\displaystyle \text{Time}=36\text{ months}=3\text{ years}

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