\displaystyle \textbf{Question 1: }\text{Ronit opened a Savings Bank Account with a bank on }16^{\text{th}}
\displaystyle \text{May, 1997 and deposited Rs. }850.\text{ He withdrew Rs. }300\text{ on }3^{\text{rd}}
\displaystyle \text{June, 1997 and thereafter made no further transactions during June.}
\displaystyle \text{Find the amount on which he would receive interest for:}
\displaystyle \text{(i) May 1997}\qquad\text{(ii) June 1997}
\displaystyle \text{Answer:}
\displaystyle \text{(i) Amount for May 1997}=\text{Rs. }0
\displaystyle \text{Reason: The account was opened after the }10^{\text{th}}\text{ of May, so no interest is payable.}
\displaystyle \text{(ii) Amount for June 1997}=\text{Rs. }550
\displaystyle \text{Balance before withdrawal}=\text{Rs. }850
\displaystyle \text{Withdrawal on }3^{\text{rd}}\text{ June}=\text{Rs. }300
\displaystyle \text{Minimum balance on or after the }10^{\text{th}}\text{ of June}=850-300=\text{Rs. }550
\\

\displaystyle \textbf{Question 2: }\text{Mr. Sharma has a Savings Bank Account with Bank of Baroda. A part}
\displaystyle \text{of his passbook is shown below:}
\displaystyle \begin{array}{|l|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{July 1, 1998} & \text{B/F} & & & 1500\\ \hline \text{July 8, 1998} & \text{By Cheque} & & 1200 & 2700\\ \hline \text{July 23, 1998} & \text{By Cash} & & 800 & 3500\\ \hline \text{Aug. 17, 1998} & \text{By Cheque} & 1600 & & 1900\\ \hline \text{Aug. 27, 1998} & \text{By Cash} & & 600 & 2500\\ \hline \end{array}
\displaystyle \text{Answer:}
\displaystyle \text{July: Minimum balance on or after the }10^{\text{th}}=\text{Rs. }2700
\displaystyle \text{August: Minimum balance on or after the }10^{\text{th}}=\text{Rs. }1900
\\

\displaystyle \textbf{Question 3: }\text{Mr. Dhoni has an account in the Union Bank of India. The following}
\displaystyle \text{entries are from his passbook:}\hfill \text{[ICSE 2008]}
\displaystyle \begin{array}{|l|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{Jan. 3, 2007} & \text{B/F} & & & 2642\\ \text{Jan. 16} & \text{To Self} & 640 & & 2002\\ \text{Mar. 5} & \text{By Cash} & & 850 & 2852\\ \text{Apr. 10} & \text{To Self} & 1130 & & 1722\\ \text{Apr. 25} & \text{By Cheque} & & 650 & 2372\\ \text{Jun. 15} & \text{By Cash} & 577 & & 1795\\ \hline \end{array}
\displaystyle \text{Calculate the interest from January 2007 to June 2007 at }4\%\text{ per annum.}
\displaystyle \text{Answer:}
\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{January} & 2002\\ \text{February} & 2002\\ \text{March} & 2852\\ \text{April} & 1722\\ \text{May} & 2372\\ \text{June} & 1795\\ \hline \text{Total} & 12745\\ \hline \end{array}
\displaystyle P=\text{Rs. }12745,\ R=4\%\text{ and }T=\frac{1}{12}\text{ year}
\displaystyle I=P\times R\times T
\displaystyle I=12745\times\frac{4}{100}\times\frac{1}{12}=\text{Rs. }42.48
\\

\displaystyle \textbf{Question 4: }\text{Divya opened a Savings Bank Account on }18^{\text{th}}\text{ October.}
\displaystyle \text{She closed the account on }18^{\text{th}}\text{ January. Calculate the interest earned}
\displaystyle \text{at }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{October} & 0\\ \text{November} & 1600\\ \text{December} & 1200\\ \text{January} & 0\\ \hline \text{Total} & 2800\\ \hline \end{array}
\displaystyle \text{No interest is payable for October as the account was opened after the }10^{\text{th}}\text{ day.}
\displaystyle \text{No interest is payable for January as the account was closed before the end of the qualifying period.}
\displaystyle P=\text{Rs. }2800,\ R=5\%\text{ and }T=\frac{1}{12}\text{ year}
\displaystyle I=P\times R\times T
\displaystyle I=2800\times\frac{5}{100}\times\frac{1}{12}=\text{Rs. }11.67
\displaystyle \therefore \text{Interest earned}=\text{Rs. }11.67
\\

\displaystyle \textbf{Question 5: }\text{Given below are the entries in a Savings Bank passbook:}
\displaystyle \begin{array}{|l|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{February 8} & \text{B/F} & - & - & 8500\\ \text{February 18} & \text{To Self} & 4000 & - & -\\ \text{April 12} & \text{By Cash} & - & 2238 & -\\ \text{June 15} & \text{To Self} & 5000 & - & -\\ \text{July 8} & \text{By Cash} & - & 6000 & -\\ \hline \end{array}
\displaystyle \text{Calculate the interest for six months, February to July, at }4\frac{1}{2}\%\text{ p.a.}
\displaystyle \text{on the minimum balance on or after the }10^{\text{th}}\text{ day of each month.}\hfill \text{[ICSE 2000, 2007]}
\displaystyle \text{Answer:}
\displaystyle \text{Completed passbook:}
\displaystyle \begin{array}{|l|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{February 8} & \text{B/F} & - & - & 8500\\ \text{February 18} & \text{To Self} & 4000 & - & 4500\\ \text{April 12} & \text{By Cash} & - & 2238 & 6738\\ \text{June 15} & \text{To Self} & 5000 & - & 1738\\ \text{July 8} & \text{By Cash} & - & 6000 & 7738\\ \hline \end{array}
\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{February} & 4500\\ \text{March} & 4500\\ \text{April} & 4500\\ \text{May} & 6738\\ \text{June} & 1738\\ \text{July} & 7738\\ \hline \text{Total} & 29714\\ \hline \end{array}
\displaystyle P=\text{Rs. }29714,\ R=4\frac{1}{2}\%\text{ and }T=\frac{1}{12}\text{ year}
\displaystyle I=P\times R\times T
\displaystyle I=29714\times\frac{9}{200}\times\frac{1}{12}
\displaystyle I=\text{Rs. }111.43
\displaystyle \therefore \text{Interest for six months}=\text{Rs. }111.43
\\

\displaystyle \textbf{Question 6: }\text{Mr. Shiv Kumar has a Savings Bank Account in Punjab National Bank.}
\displaystyle \text{His passbook has the following entries:}\hfill \text{[ICSE 2002]}
\displaystyle \begin{array}{|l|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{April 1, 1998} & \text{B/F} & - & - & 3220\\ \text{April 15} & \text{By Transfer} & - & 2010 & 5230\\ \text{May 8} & \text{To Cheque No. 355} & 298 & - & 4932\\ \text{July 15} & \text{By Clearing} & - & 4628 & 9560\\ \text{July 29} & \text{By Cash} & - & 5440 & 15000\\ \text{September 10} & \text{To Self} & 6980 & - & 8020\\ \text{January 10, 1999} & \text{By Cash} & - & 8000 & 16020\\ \hline \end{array}
\displaystyle \text{Calculate the interest due to him at the end of the financial year}
\displaystyle \text{on March }31,\ 1999\text{ at the rate of }6\%\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{April} & 3220\\ \text{May} & 4932\\ \text{June} & 4932\\ \text{July} & 4932\\ \text{August} & 15000\\ \text{September} & 8020\\ \text{October} & 8020\\ \text{November} & 8020\\ \text{December} & 8020\\ \text{January} & 16020\\ \text{February} & 16020\\ \text{March} & 16020\\ \hline \text{Total} & 113156\\ \hline \end{array}
\displaystyle P=\text{Rs. }113156,\ R=6\%\text{ and }T=\frac{1}{12}\text{ year}
\displaystyle I=P\times R\times T
\displaystyle I=113156\times\frac{6}{100}\times\frac{1}{12}
\displaystyle I=\text{Rs. }565.78
\displaystyle \therefore \text{Interest due at the end of the financial year}=\text{Rs. }565.78
\\

\displaystyle \textbf{Question 7: }\text{Given the following details, calculate simple interest at the rate}
\displaystyle \text{of }6\%\text{ per annum up to June }30.\hfill \text{[ICSE 2003]}
\displaystyle \begin{array}{|l|r|r|r|} \hline \text{Date} & \text{Debit (Rs.)} & \text{Credit (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{January 1} & - & 24000 & 24000\\ \text{January 20} & 5000 & - & 19000\\ \text{January 29} & - & 10000 & 29000\\ \text{March 15} & - & 8000 & 37000\\ \text{April 3} & - & 7653 & 44653\\ \text{May 6} & 3040 & - & 41613\\ \text{May 8} & - & 5087 & 46700\\ \hline \end{array}
\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} & 19000\\ \text{February} & 29000\\ \text{March} & 29000\\ \text{April} & 44653\\ \text{May} & 46700\\ \text{June} & 46700\\ \hline \text{Total} & 215053\\ \hline \end{array}
\displaystyle P=\text{Rs. }215053,\ R=6\%\text{ and }T=\frac{1}{12}\text{ year}
\displaystyle I=P\times R\times T
\displaystyle I=215053\times\frac{6}{100}\times\frac{1}{12}
\displaystyle I=\text{Rs. }1075.27
\displaystyle \therefore \text{Simple interest up to June 30}=\text{Rs. }1075.27
\\

\displaystyle \textbf{Question 8: }\text{If the account in Question 7 was closed on June 30, calculate the}
\displaystyle \text{interest.}
\displaystyle \text{Answer:}
\displaystyle \text{Since the account was closed on }30^{\text{th}}\text{ June, it remained active}
\displaystyle \text{throughout the qualifying period for June. Hence June also earns interest.}
\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{January} & 19000\\ \text{February} & 29000\\ \text{March} & 29000\\ \text{April} & 44653\\ \text{May} & 46700\\ \text{June} & 46700\\ \hline \text{Total} & 215053\\ \hline \end{array}
\displaystyle P=\text{Rs. }215053,\ R=6\%\text{ and }T=\frac{1}{12}\text{ year}
\displaystyle I=P\times R\times T
\displaystyle I=215053\times\frac{6}{100}\times\frac{1}{12}
\displaystyle I=\text{Rs. }1075.27
\displaystyle \therefore \text{Interest on closing the account on June 30}=\text{Rs. }1075.27
\\

\displaystyle \textbf{Question 9: }\text{The following table shows a page from the passbook of a bank:}
\displaystyle \begin{array}{|l|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{January 1, 2003} & \text{B/F} & - & - & 2842\\ \text{January 15} & \text{To Self} & 840 & - & 2002\\ \text{March 6} & \text{By Cash} & - & 856 & 2858\\ \text{April 10} & \text{To Self} & 1132 & - & 1726\\ \text{April 25} & \text{By Cheque} & - & 638 & 2364\\ \text{June 15} & \text{By Cash} & 568.50 & - & 1795.50\\ \hline \end{array}
\displaystyle \text{Calculate interest from January 2003 to June 2003 at }6\%\text{ per annum.}
\displaystyle \text{For every month, take the minimum balance to the nearest multiple}
\displaystyle \text{of Rs. }10\text{ after the }10^{\text{th}}\text{ day.}
\displaystyle \text{Answer:}
\displaystyle \begin{array}{|c|r|r|} \hline \text{Month} & \text{Principal (Rs.)} & \text{Nearest Multiple of Rs. }10\\ \hline \text{January} & 2002 & 2000\\ \text{February} & 2002 & 2000\\ \text{March} & 2858 & 2860\\ \text{April} & 1726 & 1730\\ \text{May} & 2364 & 2360\\ \text{June} & 1795.50 & 1800\\ \hline \text{Total} & 12747.50 & 12750\\ \hline \end{array}
\displaystyle P=\text{Rs. }12750,\ R=6\%\text{ and }T=\frac{1}{12}\text{ year}
\displaystyle I=P\times R\times T
\displaystyle I=12750\times\frac{6}{100}\times\frac{1}{12}
\displaystyle I=\text{Rs. }63.75
\displaystyle \therefore \text{Interest from January 2003 to June 2003}=\text{Rs. }63.75
\\

\displaystyle \textbf{Question 10: }\text{Kiran deposited Rs. }200\text{ per month for }36\text{ months in a}
\displaystyle \text{bank's Recurring Deposit Account. If the bank pays interest at }11\%
\displaystyle \text{per annum, find the amount she gets on maturity.}\hfill \text{[ICSE 2012]}
\displaystyle \text{Answer:}
\displaystyle P=\text{Rs. }200,\ r=11\%,\ n=36\text{ months}
\displaystyle \text{Interest}=P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}
\displaystyle =200\times\frac{36(36+1)}{2\times12}\times\frac{11}{100}=\text{Rs. }1221
\displaystyle \text{Total amount deposited}=P\times n=200\times36=\text{Rs. }7200
\displaystyle \text{Maturity amount}=7200+1221=\text{Rs. }8421
\\

\displaystyle \textbf{Question 11: }\text{Mohan deposited Rs. }80\text{ per month in a cumulative deposit}
\displaystyle \text{account for }6\text{ years. Find the amount payable to him on maturity if}
\displaystyle \text{the rate of interest is }6\%\text{ per annum.}\hfill \text{[ICSE 2006]}
\displaystyle \text{Answer:}
\displaystyle P=\text{Rs. }80,\ r=6\%,\ n=72\text{ months}
\displaystyle \text{Interest}=P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}
\displaystyle =80\times\frac{72(72+1)}{2\times12}\times\frac{6}{100}=\text{Rs. }1051.20
\displaystyle \text{Total amount deposited}=P\times n=80\times72=\text{Rs. }5760
\displaystyle \text{Maturity amount}=5760+1051.20=\text{Rs. }6811.20
\\

\displaystyle \textbf{Question 12: }\text{Mr. R.K. Nair gets Rs. }6455\text{ at the end of one year in a}
\displaystyle \text{Recurring Deposit Account at }14\%\text{ per annum. Find the monthly instalment.}
\displaystyle \hfill \text{[ICSE 2005]}
\displaystyle \text{Answer:}
\displaystyle \text{Let the monthly instalment be Rs. }x,\ r=14\%,\ n=12\text{ months}
\displaystyle \text{Interest}=x\times\frac{12(12+1)}{2\times12}\times\frac{14}{100}=0.91x
\displaystyle \text{Total amount deposited}=12x
\displaystyle \text{Maturity value}=12x+0.91x=12.91x
\displaystyle 12.91x=6455
\displaystyle x=\frac{6455}{12.91}=\text{Rs. }500
\displaystyle \therefore \text{Monthly instalment}=\text{Rs. }500
\\

\displaystyle \textbf{Question 13: }\text{Ahmed has a Recurring Deposit Account in a bank. He deposits}
\displaystyle \text{Rs. }2500\text{ per month for }2\text{ years. If he gets Rs. }66250\text{ at maturity,}
\displaystyle \text{find (i) the interest paid by the bank (ii) the rate of interest.}
\displaystyle \hfill \text{[ICSE 2011]}
\displaystyle \text{Answer:}
\displaystyle \text{(i) }n=24\text{ months}
\displaystyle \text{Total amount deposited}=24\times2500=\text{Rs. }60000
\displaystyle \text{Interest}=66250-60000=\text{Rs. }6250
\displaystyle \text{(ii) }P=\text{Rs. }2500,\ I=\text{Rs. }6250,\ n=24\text{ months}
\displaystyle 2500\times\frac{24(24+1)}{2\times12}\times\frac{r}{100}=6250
\displaystyle r=\frac{6250\times(2\times12)\times100}{2500\times24\times25}
\displaystyle r=10\%
\displaystyle \therefore \text{The rate of interest is }10\%\text{ per annum.}
\\

\displaystyle \textbf{Question 14: }\text{Monica has a Cumulative Deposit Account in the Union Bank of India}
\displaystyle \text{and deposits Rs. }600\text{ per month. If the maturity value is Rs. }24930
\displaystyle \text{and the rate of interest is }10\%\text{ per annum, find the time (in years)}
\displaystyle \text{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,\ r=10\%
\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}
\displaystyle 600n+600\times\frac{n(n+1)}{2\times12}\times\frac{10}{100}=24930
\displaystyle 600n+\frac{5n(n+1)}{2}=24930
\displaystyle 5n^2+1205n-49860=0
\displaystyle n^2+241n-9972=0
\displaystyle n^2+277n-36n-9972=0
\displaystyle n(n+277)-36(n+277)=0
\displaystyle (n+277)(n-36)=0
\displaystyle n=-277\text{ or }36
\displaystyle \text{Since }n\text{ cannot be negative, }n=36
\displaystyle \therefore \text{Time}=36\text{ months}=3\text{ years}
\\

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