Class 10: Banking – Exercise 4(a)

$\displaystyle \textbf{Question 1: }\text{Explain the following:}$

$\displaystyle \text{(i) A man opened a saving bank account in State Bank of India on }3\text{ Sept. 12}$
$\displaystyle \text{with Rs. }2700.\text{ He withdrew Rs. }1200\text{ on }8\text{ Sept. 12 and}$
$\displaystyle \text{deposited Rs. }500\text{ on }17\text{ Sept. } 12.\text{ If no further transactions}$
$\displaystyle \text{were made during the month, find the amount on which he would}$
$\displaystyle \text{receive interest for September 2012.}$

$\displaystyle \text{(ii) A woman opened a saving bank account in a bank on }7\text{ Nov. 08}$
$\displaystyle \text{and deposited Rs. }750.\text{ She withdrew Rs. }200\text{ on }30\text{ Nov. 08. If no}$
$\displaystyle \text{other deposit or withdrawal was made during the month, find the}$
$\displaystyle \text{amount on which she would receive interest for November 2008.}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{(i) Interest on a saving bank account is calculated on the minimum}$
$\displaystyle \text{balance between the }10^{\text{th}}\text{ day and the last day of the month.}$
$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline 3\text{-09-12} & \text{Cash} & - & 2700 & 2700\\ 8\text{-09-12} & \text{Cash} & 1200 & - & 1500\\ 10\text{-09-12} & & & & 1500\\ 17\text{-09-12} & \text{Cash} & - & 500 & 2000\\ \hline \end{array}$

$\displaystyle \text{Minimum balance from the }10^{\text{th}}\text{ day to the last day}=\text{Rs. }1500$
$\displaystyle \therefore \text{Amount on which interest is calculated}=\text{Rs. }1500$

$\displaystyle \text{(ii) Interest on a saving bank account is calculated on the minimum}$
$\displaystyle \text{balance between the }10^{\text{th}}\text{ day and the last day of the month.}$
$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline 7\text{-11-08} & \text{Cash} & - & 750 & 750\\ 10\text{-11-08} & & & & 750\\ 30\text{-11-08} & \text{Cash} & 200 & - & 550\\ \hline \end{array}$

$\displaystyle \text{Minimum balance from the }10^{\text{th}}\text{ day to the last day}=\text{Rs. }550$
$\displaystyle \therefore \text{Amount on which interest is calculated}=\text{Rs. }550$

$\\$

$\displaystyle \textbf{Question 2: }\text{A man opened a saving bank account with a bank on }22\text{ Feb. 1998}$
$\displaystyle \text{and deposited Rs. }300.\text{ He further deposited Rs. }1500\text{ on }5\text{ March 1998}$
$\displaystyle \text{and withdrew Rs. }500\text{ on }12\text{ April 1998.\text{ Assuming that he made}}$
$\displaystyle \text{no further deposits or withdrawals up to the last day of May 1998,}$
$\displaystyle \text{write the amounts on which he would receive interest for:}$
$\displaystyle \text{(i) February 1998}\qquad\text{(ii) March 1998}\qquad\text{(iii) April 1998}\qquad\text{(iv) May 1998}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Interest is calculated on the minimum balance between the }10^{\text{th}}$
$\displaystyle \text{day and the last day of each month.}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline 10\text{-02-98} & & & & 0\\ 22\text{-02-98} & \text{Cash} & - & 300 & 300\\ 28\text{-02-98} & & & & 300\\ 5\text{-03-98} & \text{Cash} & - & 1500 & 1800\\ 10\text{-03-98} & & & & 1800\\ 31\text{-03-98} & & & & 1800\\ 10\text{-04-98} & & & & 1800\\ 12\text{-04-98} & \text{Cash} & 500 & - & 1300\\ 30\text{-04-98} & & & & 1300\\ 10\text{-05-98} & & & & 1300\\ 31\text{-05-98} & & & & 1300\\ \hline \end{array}$

$\displaystyle \therefore \text{For February 1998, interest is calculated on Rs. }0$
$\displaystyle \therefore \text{For March 1998, interest is calculated on Rs. }1800$
$\displaystyle \therefore \text{For April 1998, interest is calculated on Rs. }1300$
$\displaystyle \therefore \text{For May 1998, interest is calculated on Rs. }1300$

$\\$

$\displaystyle \textbf{Question 3: }\text{A man has a saving bank account in a bank. In the months of}$
$\displaystyle \text{April 2011 and May 2011, he had the following entries in his passbook.}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{April 1} & \text{By Balance} & - & - & 4600\\ \text{April 7} & \text{By Cash} & - & 1200 & 5800\\ \text{April 24} & \text{To Cheque} & 800 & - & 5000\\ \text{May 16} & \text{By Cheque} & - & 2000 & 7000\\ \text{May 29} & \text{To Cash} & 1500 & - & 5500\\ \hline \end{array}$

$\displaystyle \text{Find the amounts on which he will get interest for the months of}$
$\displaystyle \text{April 2011 and May 2011.}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Interest is calculated on the minimum balance between the }10^{\text{th}}$
$\displaystyle \text{day and the last day of each month.}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{April 1} & \text{By Balance} & - & - & 4600\\ \text{April 7} & \text{By Cash} & - & 1200 & 5800\\ \text{April 10} & - & - & - & 5800\\ \text{April 24} & \text{To Cheque} & 800 & - & 5000\\ \text{April 30} & - & - & - & 5000\\ \text{May 10} & - & - & - & 5000\\ \text{May 16} & \text{By Cheque} & - & 2000 & 7000\\ \text{May 29} & \text{To Cash} & 1500 & - & 5500\\ \text{May 31} & - & - & - & 5500\\ \hline \end{array}$

$\displaystyle \text{For April 2011, minimum balance from }10^{\text{th}}\text{ April to }30^{\text{th}}\text{ April}=\text{Rs. }5000$

$\displaystyle \therefore \text{Amount on which interest is calculated for April 2011}=\text{Rs. }5000$

$\displaystyle \text{For May 2011, minimum balance from }10^{\text{th}}\text{ May to }31^{\text{st}}\text{ May}=\text{Rs. }5000$

$\displaystyle \therefore \text{Amount on which interest is calculated for May 2011}=\text{Rs. }5000$

$\\$

$\displaystyle \textbf{Question 4: }\text{A page from the passbook of a woman is given below:}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{Jan. 5} & \text{Balance B/F} & - & - & 3750\\ \text{March 7} & \text{To Cheque} & 1200 & - & -\\ \text{April 2} & \text{By Cheque} & - & 2300 & -\\ \text{April 10} & \text{By Cheque} & - & 820 & -\\ \text{Oct. 6} & \text{To Cheque} & 950 & - & -\\ \text{Dec. 8} & \text{By Cash} & - & 1700 & -\\ \hline \end{array}$

$\displaystyle \text{Complete the passbook and then calculate the interest for the period}$
$\displaystyle \text{January to December at }5\%\text{ per annum.}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Completed passbook:}$

$\displaystyle \text{Interest is calculated on the minimum balance between the }10^{\text{th}}$
$\displaystyle \text{day and the last day of each month.}$

$\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{January} & 3750\\ \text{February} & 3750\\ \text{March} & 2550\\ \text{April} & 5670\\ \text{May} & 5670\\ \text{June} & 5670\\ \text{July} & 5670\\ \text{August} & 5670\\ \text{September} & 5670\\ \text{October} & 4720\\ \text{November} & 4720\\ \text{December} & 6420\\ \hline \text{Total} & 59930\\ \hline \end{array}$

$\displaystyle \text{Here, }P=\text{Rs. }59930,\ R=5\%\text{ and }T=\frac{1}{12}\text{ year}$

$\displaystyle I=P\times R\times T$

$\displaystyle I=59930\times\frac{5}{100}\times\frac{1}{12}$

$\displaystyle I=\text{Rs. }249.71$

$\displaystyle \therefore \text{Interest for the period January to December}=\text{Rs. }249.71$

$\\$

$\displaystyle \textbf{Question 5: }\text{The entries in a Saving Bank passbook are given below:}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline 01.01.03 & \text{B/F} & - & - & 14000\\ 01.02.03 & \text{By Cash} & - & 11500 & 25500\\ 12.02.03 & \text{To Cheque} & 5000 & - & 20500\\ 05.04.03 & \text{By Cash} & - & 3750 & 24250\\ 15.04.03 & \text{To Cheque} & 4250 & - & 20000\\ 09.05.03 & \text{By Cash} & - & 1500 & 21500\\ 04.06.03 & \text{By Cash} & - & 1500 & 23000\\ \hline \end{array}$

$\displaystyle \text{Calculate the interest for six months, January to June, at }4\%\text{ per annum}$
$\displaystyle \text{on the minimum balance on or after the tenth day of each month.}\hfill \text{[ICSE 2004]}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}$
$\displaystyle \text{day of each month.}$

$\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{January} & 14000\\ \text{February} & 20500\\ \text{March} & 20500\\ \text{April} & 20000\\ \text{May} & 21500\\ \text{June} & 23000\\ \hline \text{Total} & 119500\\ \hline \end{array}$

$\displaystyle \text{Here, }P=\text{Rs. }119500,\ R=4\%\text{ and }T=\frac{1}{12}\text{ year}$

$\displaystyle I=P\times R\times T$

$\displaystyle I=119500\times\frac{4}{100}\times\frac{1}{12}$

$\displaystyle I=\text{Rs. }398.33$

$\displaystyle \therefore \text{Interest for six months}=\text{Rs. }398.33$

$\\$

$\displaystyle \textbf{Question 6: }\text{A page from the passbook of Mrs. Rama Bhalla is given below:}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date (Year 2004)} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{January 1} & \text{B/F} & - & - & 2000\\ \text{January 9} & \text{By Cash} & - & 200 & 2200\\ \text{February 10} & \text{To Cheque} & 500 & - & 1700\\ \text{February 24} & \text{By Cheque} & - & 300 & 2000\\ \text{July 29} & \text{To Cheque} & 200 & - & 1800\\ \text{November 7} & \text{By Cash} & - & 300 & 2100\\ \text{December 8} & \text{By Cash} & - & 200 & 2300\\ \hline \end{array}$

$\displaystyle \text{Calculate the interest to Mrs. Rama Bhalla for the period January 2004}$
$\displaystyle \text{to December 2004 at the rate of }5\%\text{ per annum.}\hfill \text{[ICSE 2005]}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}$
$\displaystyle \text{day of each month.}$

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

$\displaystyle \text{Here, }P=\text{Rs. }23500,\ R=5\%\text{ and }T=\frac{1}{12}\text{ year}$

$\displaystyle I=P\times R\times T$

$\displaystyle I=23500\times\frac{5}{100}\times\frac{1}{12}$

$\displaystyle I=\text{Rs. }97.92$

$\displaystyle \therefore \text{Interest for the period January to December 2004}=\text{Rs. }97.92$

$\\$

$\displaystyle \textbf{Question 7: }\text{A man has a Saving Bank account with the Post Office.}$

$\displaystyle \text{Calculate the interest earned by him during the year 2010 at }6.5\%\text{ per annum,}$
$\displaystyle \text{payable in December, if the entries in his passbook are as given below:}$

$\displaystyle \begin{array}{|c|l|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)}\\ \hline 2.1.10 & \text{By Cash} & - & 250\\ 9.1.10 & \text{By Cheque} & - & 825\\ 13.3.10 & \text{To Cash} & 325 & -\\ 24.7.10 & \text{By Cash} & - & 1237\\ 6.10.10 & \text{To Cheque} & 250 & -\\ 22.12.10 & \text{By Cheque} & - & 958\\ \hline \end{array}$

$\displaystyle \text{Also calculate the interest when the principal for every month is}$
$\displaystyle \text{taken as the nearest multiple of Rs. }10.$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Completed passbook:}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline 2.1.10 & \text{By Cash} & - & 250 & 250\\ 9.1.10 & \text{By Cheque} & - & 825 & 1075\\ 13.3.10 & \text{To Cash} & 325 & - & 750\\ 24.7.10 & \text{By Cash} & - & 1237 & 1987\\ 6.10.10 & \text{To Cheque} & 250 & - & 1737\\ 22.12.10 & \text{By Cheque} & - & 958 & 2695\\ \hline \end{array}$

$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}$
$\displaystyle \text{day of each month.}$

$\displaystyle \begin{array}{|c|r|r|} \hline \text{Month} & \text{Principal (Rs.)} & \text{Nearest Multiple of Rs. }10\\ \hline \text{January} & 1075 & 1080\\ \text{February} & 1075 & 1080\\ \text{March} & 750 & 750\\ \text{April} & 750 & 750\\ \text{May} & 750 & 750\\ \text{June} & 750 & 750\\ \text{July} & 750 & 750\\ \text{August} & 1987 & 1990\\ \text{September} & 1987 & 1990\\ \text{October} & 1737 & 1740\\ \text{November} & 1737 & 1740\\ \text{December} & 1737 & 1740\\ \hline \text{Total} & 15085 & 15110\\ \hline \end{array}$

$\displaystyle \text{(i) Without rounding the monthly principal:}$

$\displaystyle P=\text{Rs. }15085,\ R=6.5\%\text{ and }T=\frac{1}{12}\text{ year}$

$\displaystyle I=P\times R\times T$

$\displaystyle I=15085\times\frac{6.5}{100}\times\frac{1}{12}$

$\displaystyle I=\text{Rs. }81.71$

$\displaystyle \text{(ii) Taking the monthly principal as the nearest multiple of Rs. }10:$

$\displaystyle P=\text{Rs. }15110,\ R=6.5\%\text{ and }T=\frac{1}{12}\text{ year}$

$\displaystyle I=P\times R\times T$

$\displaystyle I=15110\times\frac{6.5}{100}\times\frac{1}{12}$

$\displaystyle I=\text{Rs. }81.85$

$\\$

$\displaystyle \textbf{Question 8: }\text{A Saving Bank account was opened by a woman on }3.7.12$
$\displaystyle \text{and closed on }31.01.13.\text{ The entries in the passbook were as given below:}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline 3.7.12 & \text{By Cash} & - & 690 & -\\ 15.7.12 & \text{By Cash} & - & 1153 & -\\ 27.8.12 & \text{By Cheque} & - & 2468 & -\\ 30.8.12 & \text{To Cash} & 946 & - & -\\ 12.9.12 & \text{To Cheque} & 1000 & - & -\\ 20.11.12 & \text{By Cheque} & - & 3000 & -\\ 26.11.12 & \text{By Cash} & - & 750 & -\\ 28.11.12 & \text{To Cash} & 1570 & - & -\\ \hline \end{array}$

$\displaystyle \text{By finding the balance on different dates of entries, calculate the}$
$\displaystyle \text{interest earned by her for the period she had this Saving Bank account}$
$\displaystyle \text{at the rate of }6\%\text{ per annum.}$

$\displaystyle \text{Also, calculate the interest when the principal for every month is taken}$
$\displaystyle \text{as the nearest multiple of Rs. }10.$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Completed passbook:}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline 3.7.12 & \text{By Cash} & - & 690 & 690\\ 15.7.12 & \text{By Cash} & - & 1153 & 1843\\ 27.8.12 & \text{By Cheque} & - & 2468 & 4311\\ 30.8.12 & \text{To Cash} & 946 & - & 3365\\ 12.9.12 & \text{To Cheque} & 1000 & - & 2365\\ 20.11.12 & \text{By Cheque} & - & 3000 & 5365\\ 26.11.12 & \text{By Cash} & - & 750 & 6115\\ 28.11.12 & \text{To Cash} & 1570 & - & 4545\\ \hline \end{array}$

$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}$
$\displaystyle \text{day of each month.}$

$\displaystyle \begin{array}{|c|r|r|} \hline \text{Month} & \text{Principal (Rs.)} & \text{Nearest Multiple of Rs. }10\\ \hline \text{July} & 690 & 690\\ \text{August} & 1843 & 1840\\ \text{September} & 2365 & 2370\\ \text{October} & 2365 & 2370\\ \text{November} & 2365 & 2370\\ \text{December} & 4545 & 4550\\ \text{January} & 4545 & 4550\\ \hline \text{Total} & 18718 & 18740\\ \hline \end{array}$

$\displaystyle \text{(i) Without rounding the monthly principal:}$

$\displaystyle P=\text{Rs. }18718,\ R=6\%\text{ and }T=\frac{1}{12}\text{ year}$

$\displaystyle I=P\times R\times T$

$\displaystyle I=18718\times\frac{6}{100}\times\frac{1}{12}$

$\displaystyle I=\text{Rs. }93.59$

$\displaystyle \text{(ii) Taking the monthly principal as the nearest multiple of Rs. }10:$

$\displaystyle P=\text{Rs. }18740,\ R=6\%\text{ and }T=\frac{1}{12}\text{ year}$

$\displaystyle I=P\times R\times T$

$\displaystyle I=18740\times\frac{6}{100}\times\frac{1}{12}$

$\displaystyle I=\text{Rs. }93.70$

$\\$

$\displaystyle \textbf{Question 9: }\text{A man had a saving Bank account with the State Bank of India,}$
$\displaystyle \text{from }13^{\text{th}}\text{ Feb. 09 to }6^{\text{th}}\text{ August 09. The following table shows}$
$\displaystyle \text{the entries in his passbook for the above period. Calculate the interest}$
$\displaystyle \text{earned by him on his S.B. Account up to }31^{\text{st}}\text{ July, 09 at }5\%\text{ p.a.}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{Feb. 13} & \text{By Cash} & - & 500 & 500\\ \text{March 3} & \text{By Cheque} & - & 735 & 1235\\ \text{March 14} & \text{By Cheque} & - & 1040 & 2275\\ \text{May 10} & \text{To Cheque} & 240 & - & 2035\\ \text{May 22} & \text{To Cash} & 430 & - & 1605\\ \text{June 09} & \text{By Cash} & - & 780 & 2385\\ \text{July 26} & \text{To Cash} & 980 & - & 1405\\ \hline \end{array}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}$
$\displaystyle \text{day of each month.}$

$\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{February} & 0\\ \text{March} & 1235\\ \text{April} & 2275\\ \text{May} & 1605\\ \text{June} & 2385\\ \text{July} & 1405\\ \hline \text{Total} & 8905\\ \hline \end{array}$

$\displaystyle P=\text{Rs. }8905,\ R=5\%\text{ and }T=\frac{1}{12}\text{ year}$

$\displaystyle I=P\times R\times T$

$\displaystyle I=8905\times\frac{5}{100}\times\frac{1}{12}$

$\displaystyle I=\text{Rs. }37.10$

$\displaystyle \therefore \text{Interest earned up to }31^{\text{st}}\text{ July, 09}=\text{Rs. }37.10$

$\\$

$\displaystyle \textbf{Question 10: }\text{A page from the passbook of a saving bank account in a particular}$
$\displaystyle \text{year is given below:}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Debit (Rs.)} & \text{Credit (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{Jan. 3} & \text{By Cash} & - & 5000 & 5000\\ \text{Feb. 13} & \text{To Self} & 500 & - & -\\ \text{March 24} & \text{By Cheque} & - & 2000 & -\\ \text{March 31} & \text{By Interest} & - & - & -\\ \text{May 20} & \text{By Cash} & - & 800 & -\\ \text{July 7} & \text{To Cheque} & 1400 & - & -\\ \text{July 18} & \text{By Cash} & - & 1600 & -\\ \text{Sept. 15} & \text{To Cheque} & 3200 & - & -\\ \text{Sept. 26} & \text{By Cheque} & - & 2350 & -\\ \hline \end{array}$

$\displaystyle \text{If the interest is calculated at }6\%\text{ p.a. and is compounded at the end}$
$\displaystyle \text{of March and September every year, find the interest earned up to }31^{\text{st}}\text{ March.}$
$\displaystyle \text{Then complete all the entries and find the amount the account holder}$
$\displaystyle \text{would receive if he closed the account on }20^{\text{th}}\text{ October of the same year.}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Completed passbook:}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Debit (Rs.)} & \text{Credit (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{Jan. 3} & \text{By Cash} & - & 5000 & 5000\\ \text{Feb. 13} & \text{To Self} & 500 & - & 4500\\ \text{March 24} & \text{By Cheque} & - & 2000 & 6500\\ \text{March 31} & \text{By Interest} & - & 70 & 6570\\ \text{May 20} & \text{By Cash} & - & 800 & 7370\\ \text{July 7} & \text{To Cheque} & 1400 & - & 5970\\ \text{July 18} & \text{By Cash} & - & 1600 & 7570\\ \text{Sept. 15} & \text{To Cheque} & 3200 & - & 4370\\ \text{Sept. 26} & \text{By Cheque} & - & 2350 & 6720\\ \text{Sept. 30} & \text{By Interest} & - & 192.10 & 6912.10\\ \hline \end{array}$

$\displaystyle \text{Interest up to }31^{\text{st}}\text{ March:}$

$\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{January} & 5000\\ \text{February} & 4500\\ \text{March} & 4500\\ \hline \text{Total} & 14000\\ \hline \end{array}$

$\displaystyle P=\text{Rs. }14000,\ R=6\%\text{ and }T=\frac{1}{12}\text{ year}$

$\displaystyle I=14000\times\frac{6}{100}\times\frac{1}{12}$

$\displaystyle I=\text{Rs. }70$

$\displaystyle \text{Qualifying principal from April to September:}$

$\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{April} & 6570\\ \text{May} & 6570\\ \text{June} & 7370\\ \text{July} & 5970\\ \text{August} & 7570\\ \text{September} & 4370\\ \hline \text{Total} & 38420\\ \hline \end{array}$

$\displaystyle \text{Interest up to }30^{\text{th}}\text{ September:}$

$\displaystyle P=\text{Rs. }38420,\ R=6\%\text{ and }T=\frac{1}{12}\text{ year}$

$\displaystyle I=38420\times\frac{6}{100}\times\frac{1}{12}$

$\displaystyle I=\text{Rs. }192.10$

$\displaystyle \text{Amount received on closing the account on }20^{\text{th}}\text{ October}$

$\displaystyle =\text{Rs. }6720+\text{Rs. }192.10$

$\displaystyle =\text{Rs. }6912.10$

$\\$

$\displaystyle \textbf{Question 11: }\text{A page from the Saving Bank account of Mr. Prateek is given below:}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{Jan. 1, 2006} & \text{B/F} & - & - & 1270\\ \text{Jan. 7, 2006} & \text{By Cheque} & - & 2310 & 3580\\ \text{Mar. 9, 2006} & \text{To Self} & 2000 & - & 1580\\ \text{Mar. 26, 2006} & \text{By Cash} & - & 6200 & 7780\\ \text{Jun. 10, 2006} & \text{To Cheque} & 4500 & - & 3280\\ \text{Jul. 15, 2006} & \text{By Clearing} & - & 2630 & 5910\\ \text{Oct. 18, 2006} & \text{To Cheque} & 530 & - & 5380\\ \text{Oct. 27, 2006} & \text{To Self} & 2690 & - & 2690\\ \text{Nov. 3, 2006} & \text{By Cash} & - & 1500 & 4190\\ \text{Dec. 6, 2006} & \text{To Cheque} & 950 & - & 3240\\ \text{Dec. 23, 2006} & \text{By Transfer} & - & 2920 & 6160\\ \hline \end{array}$

$\displaystyle \text{If he receives Rs. }198\text{ as interest on }1^{\text{st}}\text{ January 2007, find the}$
$\displaystyle \text{rate of interest paid by the bank.}\hfill \text{[ICSE 2012]}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}$
$\displaystyle \text{day of each month.}$

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

$\displaystyle \text{Let the rate of interest be }x\%\text{ per annum.}$

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

$\displaystyle I=P\times\frac{R}{100}\times T$

$\displaystyle 198=52800\times\frac{x}{100}\times\frac{1}{12}$

$\displaystyle 198=44x$

$\displaystyle x=\frac{198}{44}=4.5\%$

$\displaystyle \therefore \text{The rate of interest paid by the bank is }4.5\%\text{ per annum.}$

$\\$

$\displaystyle \textbf{Question 12: }\text{A man holds a Saving Bank account in the Union Bank of India.}$
$\displaystyle \text{A page of his passbook shows the following entries:}$

$\displaystyle \text{Calculate the rate of interest per annum if the total interest earned}$
$\displaystyle \text{for the months of May and June is Rs. }39.25.$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}$
$\displaystyle \text{day of each month.}$

$\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{May} & 3700\\ \text{June} & 4150\\ \hline \text{Total} & 7850\\ \hline \end{array}$

$\displaystyle \text{Let the rate of interest be }x\%\text{ per annum.}$

$\displaystyle P=\text{Rs. }7850,\ R=x\%,\ T=\frac{1}{12}\text{ year and }I=\text{Rs. }39.25$

$\displaystyle I=P\times\frac{R}{100}\times T$

$\displaystyle 39.25=7850\times\frac{x}{100}\times\frac{1}{12}$

$\displaystyle 39.25=\frac{7850x}{1200}$

$\displaystyle x=\frac{39.25\times1200}{7850}=6\%$

$\displaystyle \therefore \text{The rate of interest is }6\%\text{ per annum.}$

$\\$

$\displaystyle \textbf{Question 13: }\text{A page from the passbook of a man is given below. The interest}$
$\displaystyle \text{accrued for the period January to December 2006 at a certain rate}$
$\displaystyle \text{of interest p.a. is Rs. }377.40.\text{ Without taking the principal as the}$
$\displaystyle \text{nearest multiple of Rs. }10,\text{ calculate the rate.}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date 2006} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{Jan. 1} & \text{By Balance} & - & - & 7500\\ \text{March 7} & \text{By Cheque} & - & 1875 & -\\ \text{March 10} & \text{By Cash} & - & 625 & -\\ \text{July 17} & \text{To Self} & 3250 & - & -\\ \text{Oct. 5} & \text{By Cheque} & - & 2160 & -\\ \text{Dec. 19} & \text{To Cheque} & 1340 & - & -\\ \hline \end{array}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Completed passbook:}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date 2006} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline \text{Jan. 1} & \text{By Balance} & - & - & 7500\\ \text{March 7} & \text{By Cheque} & - & 1875 & 9375\\ \text{March 10} & \text{By Cash} & - & 625 & 10000\\ \text{July 17} & \text{To Self} & 3250 & - & 6750\\ \text{Oct. 5} & \text{By Cheque} & - & 2160 & 8910\\ \text{Dec. 19} & \text{To Cheque} & 1340 & - & 7570\\ \hline \end{array}$

$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}$
$\displaystyle \text{day of each month.}$

$\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{January} & 7500\\ \text{February} & 7500\\ \text{March} & 10000\\ \text{April} & 10000\\ \text{May} & 10000\\ \text{June} & 10000\\ \text{July} & 6750\\ \text{August} & 6750\\ \text{September} & 6750\\ \text{October} & 8910\\ \text{November} & 8910\\ \text{December} & 7570\\ \hline \text{Total} & 100640\\ \hline \end{array}$

$\displaystyle \text{Let the rate of interest be }x\%\text{ per annum.}$

$\displaystyle P=\text{Rs. }100640,\ R=x\%,\ T=\frac{1}{12}\text{ year and }I=\text{Rs. }377.40$

$\displaystyle I=P\times\frac{R}{100}\times T$

$\displaystyle 377.40=100640\times\frac{x}{100}\times\frac{1}{12}$

$\displaystyle 377.40=\frac{100640x}{1200}$

$\displaystyle x=\frac{377.40\times1200}{100640}=4.5\%$

$\displaystyle \therefore \text{The rate of interest is }4.5\%\text{ per annum.}$

$\\$

$\displaystyle \textbf{Question 14: }\text{A man opened a Saving Bank Account with the State Bank of India}$
$\displaystyle \text{on }5^{\text{th}}\text{ April 2007 with Rs. }8500.\text{ For the financial year 2007-2008,}$
$\displaystyle \text{the other transactions with the bank were as follows:}$

$\displaystyle \begin{array}{l} \text{15-05-2007 : Deposited Rs. }3700\\ \text{27-07-2007 : Withdrew Rs. }2400\\ \text{06-09-2007 : Withdrew Rs. }1600\\ \text{18-12-2007 : Deposited Rs. }4500\\ \text{29-01-2008 : Deposited Rs. }1900\\ \text{23-03-2008 : Account closed} \end{array}$

$\displaystyle \text{Taking the rate of interest as }6\%\text{ per annum, find the amount}$
$\displaystyle \text{that he gets on closing the account.}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Completed passbook:}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline 5\text{-04-2007} & \text{Cash} & - & 8500 & 8500\\ 15\text{-05-2007} & \text{Cash} & - & 3700 & 12200\\ 27\text{-07-2007} & \text{Cash} & 2400 & - & 9800\\ 06\text{-09-2007} & \text{Cash} & 1600 & - & 8200\\ 18\text{-12-2007} & \text{Cash} & - & 4500 & 12700\\ 29\text{-01-2008} & \text{Cash} & - & 1900 & 14600\\ 23\text{-03-2008} & \text{Account Closed} & - & - & -\\ \hline \end{array}$

$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}$
$\displaystyle \text{day of each month.}$

$\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{April} & 8500\\ \text{May} & 8500\\ \text{June} & 12200\\ \text{July} & 9800\\ \text{August} & 9800\\ \text{September} & 8200\\ \text{October} & 8200\\ \text{November} & 8200\\ \text{December} & 8200\\ \text{January} & 12700\\ \text{February} & 14600\\ \hline \text{Total} & 108900\\ \hline \end{array}$

$\displaystyle \text{Here, }P=\text{Rs. }108900,\ R=6\%\text{ and }T=\frac{1}{12}\text{ year}$

$\displaystyle I=P\times R\times T$

$\displaystyle I=108900\times\frac{6}{100}\times\frac{1}{12}$

$\displaystyle I=\text{Rs. }544.50$

$\displaystyle \text{Amount received on closing the account}$

$\displaystyle =\text{Rs. }14600+\text{Rs. }544.50$

$\displaystyle =\text{Rs. }15144.50$

$\\$

$\displaystyle \textbf{Question 15: }\text{A woman has a saving bank account with the Punjab National Bank.}$
$\displaystyle \text{She had the following transactions from }1^{\text{st}}\text{ January 2007 to }31^{\text{st}}\text{ December 2007:}$

$\displaystyle \begin{array}{l} \text{01-01-2007 : B/F Rs. }8764\\ \text{13-03-2007 : Deposited Rs. }6482\\ \text{22-06-2007 : Withdrew Rs. }4369\\ \text{09-08-2007 : Withdrew Rs. }1333\\ \text{24-11-2007 : Deposited Rs. }2158 \end{array}$

$\displaystyle \text{Calculate the interest accrued up to }31^{\text{st}}\text{ December 2007, if the}$
$\displaystyle \text{rate of interest is }5\%\text{ compounded yearly and the principal for every}$
$\displaystyle \text{month is taken as the nearest multiple of Rs. }10.$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Completed passbook:}$

$\displaystyle \begin{array}{|c|l|r|r|r|} \hline \text{Date} & \text{Particulars} & \text{Withdrawals (Rs.)} & \text{Deposits (Rs.)} & \text{Balance (Rs.)}\\ \hline 01\text{-01-2007} & \text{B/F} & - & - & 8764\\ 13\text{-03-2007} & \text{Cash} & - & 6482 & 15246\\ 22\text{-06-2007} & \text{Cash} & 4369 & - & 10877\\ 09\text{-08-2007} & \text{Cash} & 1333 & - & 9544\\ 24\text{-11-2007} & \text{Cash} & - & 2158 & 11702\\ \hline \end{array}$

$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}$
$\displaystyle \text{day of each month.}$

$\displaystyle \begin{array}{|c|r|r|} \hline \text{Month} & \text{Principal (Rs.)} & \text{Nearest Multiple of Rs. }10\\ \hline \text{January} & 8764 & 8760\\ \text{February} & 8764 & 8760\\ \text{March} & 8764 & 8760\\ \text{April} & 15246 & 15250\\ \text{May} & 15246 & 15250\\ \text{June} & 10877 & 10880\\ \text{July} & 10877 & 10880\\ \text{August} & 9544 & 9540\\ \text{September} & 9544 & 9540\\ \text{October} & 9544 & 9540\\ \text{November} & 9544 & 9540\\ \text{December} & 11702 & 11700\\ \hline \text{Total} & 128416 & 128400\\ \hline \end{array}$

$\displaystyle \text{Here, }P=\text{Rs. }128400,\ R=5\%\text{ and }T=\frac{1}{12}\text{ year}$

$\displaystyle I=P\times R\times T$

$\displaystyle I=128400\times\frac{5}{100}\times\frac{1}{12}$

$\displaystyle I=\text{Rs. }535$

$\displaystyle \therefore \text{Interest accrued up to }31^{\text{st}}\text{ December 2007}=\text{Rs. }535$

$\\$

$\displaystyle \textbf{Question 16: }\text{Mrs. Kapoor opened a Saving Bank Account in the State Bank of India}$
$\displaystyle \text{on }9^{\text{th}}\text{ January 2008. Her passbook entries for the year 2008 are}$
$\displaystyle \text{given below:}\hfill \text{[ICSE 2010]}$

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

$\displaystyle \text{Mrs. Kapoor closed the account on }31^{\text{st}}\text{ December 2008. If the bank}$
$\displaystyle \text{pays interest at }4\%\text{ per annum, find the interest she receives on}$
$\displaystyle \text{closing the account. Give your answer correct to the nearest rupee.}$

$\displaystyle \text{Answer:}$

$\displaystyle \text{Interest is calculated on the minimum balance on or after the }10^{\text{th}}$
$\displaystyle \text{day of each month.}$

$\displaystyle \begin{array}{|c|r|} \hline \text{Month} & \text{Principal (Rs.)}\\ \hline \text{January} & 10000\\ \text{February} & 10000\\ \text{March} & 25500\\ \text{April} & 20000\\ \text{May} & 20000\\ \text{June} & 20000\\ \text{July} & 20000\\ \text{August} & 19800\\ \text{September} & 19800\\ \text{October} & 19800\\ \text{November} & 19800\\ \text{December} & 21500\\ \hline \text{Total} & 226200\\ \hline \end{array}$

$\displaystyle \text{Here, }P=\text{Rs. }226200,\ R=4\%\text{ and }T=\frac{1}{12}\text{ year}$

$\displaystyle I=P\times R\times T$

$\displaystyle I=226200\times\frac{4}{100}\times\frac{1}{12}$

$\displaystyle I=\text{Rs. }754$

$\displaystyle \therefore \text{Interest received on closing the account}=\text{Rs. }754$

$\\$

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Class 10: Banking – Exercise 4(a)

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