Class 10: Banking – Miscellaneous Problems-Set 1 – ICSE / ISC / CBSE Mathematics Portal for K12 Students

Question 1: Ronit opened a savings bank account with a bank on l6th 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 197. What is the amount on which he would receive the intere.st of : (i) May 1997 ? (ii) June 1997?

Answer:

(i) The amount on which he would receive interest for May 1997 = Nil i.e. Rs. 0

Reason :

Whenever an account, with the bank, is opened after 10th of any month; the amount qualifying for interest for that month is Rs. 0.

(ii) The amount on which he would receive the interest of June 1997 = Rs. 550

Reason :
Up to 3rd June, 1t997, the amount to his credit = Rs. 850

On 3rd June, 1997, he withdrew Rs. 300.

Therefore From 3rd June, 1997 to the last day of June, 97 the minimum amount to his credit = 850 – 300 = Rs. 550.

Therefore On 10th June, 1997 and up to the last day of June, 97 the minimum amount to his credit = Rs. 550

Therefore the amount qualifying for interest for the month of June, 97 = Rs. 550

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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:

$\begin{array} {|l |l |r |r |r | } \hline \text{Date} & \text{Particulars} & \text{Amount } & \text{Amount } & \text{Balance (Rs.)} \\ & &\text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \\ \hline \text{July 1, 98} & \text{B/F } & & & 1500.00 \\ \hline \text{July 8, 98} & \text{By Cheque} & & 1200.00 & 2700.00 \\ \hline \text{July 23, 98} & \text{By Cash} & & 800.00 & 3500.00 \\ \hline \text{Aug. 17, 98} & \text{By Cheque} &1600.00 & & 1900.00 \\ \hline \text{Aug. 27, 98} & \text{By Cash} & & 600.00 & 2500.00 \\ \hline \end{array}$

Find the amounts on which he will get interest for the months of July, 98 and Aug., 98.

Answer:

Since, the minimum balance on 10th July, 98 and up to the last day of July, 98 is Rs. 2700.

Therefore the amount on which Mr. Sharma will earn interest for the month of July, 98 = Rs. 2700.00

Similarly, it is clear from the passbook, that the minimum amount to Mr. Sharma’s credit on 10th August, 98 and up to the last day of August, 98 is Rs. 1900.00

The amount on which he will earn interest for the month of Aug., 98 = Rs. 1900.00

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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]

Answer:

Qualifying principal for various months :

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

$\displaystyle P = \text{ Rs. } 12745, \hspace{1.0cm} R = 4\% , \hspace{1.0cm} T = \frac{1}{12} \text{ year }$

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

$\\$

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.

Answer:

Since, Divya opened her account on 18th Oct.

$\displaystyle \text{Principal for the month of October } = \text{ Rs. } 00.00$

$\displaystyle \text{Principal for the month of November } = \text{ Rs. } 1600.00$

$\displaystyle \text{and, principal for the month of December } = \text{ Rs. }.1200.00$

$\displaystyle \text{Total principal } = 1600.00 + 1200.00 =\text{ Rs. } 2800.00$

She will not get any interest for the month of January as she does not keep her account in the bank for the whole of January.

$\displaystyle P = \text{ Rs. } 2800, \hspace{1.0cm} R = 5\% , \hspace{1.0cm} T = \frac{1}{12} \text{ year }$

$\displaystyle \text{Interest } = \frac{P \times R \times T}{100} = \frac{2800 \times 5 \times 1}{100 \times 12} = \text{ Rs. } 11.67$

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Question 5: Given below are the entries in a savings Bank a passbook:

Calculate the interest for the six months, February to July, at $4 \frac{1}{2}\%$ p.a. on the minimum balance on or after the 10th day of each month. [ ICSE Board 2000, 2007]

Answer:

On completing the given table, we get:

So, qualifying principal for various months:

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

$\displaystyle P = \text{ Rs. } 29714, \hspace{1.0cm} R = 4\frac{1}{2}\% , \hspace{1.0cm} T = \frac{1}{12} \text{ year }$

$\displaystyle \text{Interest } = \frac{P \times R \times T}{100} = \frac{29714 \times 9 \times 1}{100 \times 2 \times 12} = \text{ Rs. } 111.43$

When the principal is taken correct to nearest multiple of Rs. 10:

$\begin{array}{|l|c| c| } \hline \text{Month} & \text{Principal (Rs.) } & \text{ Principal correct to nearest multiple of Rs. 10} \\ \hline \text{February } & 4500 & 4500 \\ \hline \text{March } & 4500 & 4500 \\ \hline \text{April } & 4500 & 4500 \\ \hline \text{May } & 6738 & 6740 \\ \hline \text{June } & 1738 & 1740\\ \hline \text{July } & 7738 & 7740 \\ \hline \text{Total } & 29714 & 29720 \\ \hline \end{array}$

$\displaystyle P = \text{ Rs. } 29720, \hspace{1.0cm} R = 4\frac{1}{2}\% , \hspace{1.0cm} T = \frac{1}{12} \text{ year }$

$\displaystyle \text{Interest } = \frac{P \times R \times T}{100} = \frac{29720 \times 9 \times 1}{100 \times 2 \times 12} = \text{ Rs. } 111.45$

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Question 6: Mr. Shiv Kumar has a Savings Bank Account in the Punjab National Bank. His passbook has the following entries:

$\begin{array} {|l |l |r |r |r | } \hline \text{Date} & \text{Particulars} & \text{Amount } & \text{Amount } & \text{Balance (Rs.)} \\ & &\text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \\ \hline \text{April 1, 1998 } & \text{B/F } & & & 3220.00 \\ \hline \text{April 15} & \text{By Transfer} & & 2010.00 & 5230.00 \\ \hline \text{May 8} & \text{To Cheque No355} & 298.00 & & 4932.00 \\ \hline \text{July 15} & \text{By Clearing} & & 4628.00 & 9560.00 \\ \hline \text{July 29} & \text{By Cash} & & 5440.00 & 15000.00 \\ \hline \text{September 10} & \text{To Self} & 6980.00 & & 8020.00 \\ \hline \text{January 10, 1998} & \text{By Cash} & & 8000.00 & 16020.00 \\ \hline \end{array}$

Calculate the interest due to him at the end of the financial year ( March 31st 1998) at the rate of 6% per annum. [ ICSE Board 2002]

Answer:

Qualifying principal for various months :

$\begin{array}{|l|c| c| } \hline \text{Month} & \text{Principal (Rs.) } & \text{ Principal correct to nearest multiple of Rs. 10} \\ \hline \text{April } & 3220 & 3220 \\ \hline \text{May } & 4932 & 4930 \\ \hline \text{June } & 4932 & 4930\\ \hline \text{July } & 4932 & 4930 \\ \hline \text{August } & 15000 & 15000 \\ \hline \text{September } & 8020 & 8020 \\ \hline \text{October } & 8020 & 8020 \\ \hline \text{November } & 8020 & 8020 \\ \hline \text{December } & 8020 & 8020 \\ \hline \text{January } & 16020 & 16020 \\ \hline \text{February } & 16020 & 16020 \\ \hline \text{March } &16020 & 16020 \\ \hline \text{Total } & 113156 & 113150 \\ \hline \end{array}$

When the principal is not rounded off

$\displaystyle P = \text{ Rs. } 113156, \hspace{1.0cm} R = 6\% , \hspace{1.0cm} T = \frac{1}{12} \text{ year }$

$\displaystyle \text{Interest } = \frac{P \times R \times T}{100} = \frac{113156 \times 6 \times 1}{100 \times 12} = \text{ Rs. } 565.78$

When the principal is taken correct to nearest multiple of Rs. 10

$\displaystyle P = \text{ Rs. } 113150, \hspace{1.0cm} R = 6\% , \hspace{1.0cm} T = \frac{1}{12} \text{ year }$

$\displaystyle \text{Interest } = \frac{P \times R \times T}{100} = \frac{113150 \times 6 \times 1}{100 \times 12} = \text{ Rs. } 565.75$

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Question 7: Given the following details, calculate simple interest at the rate of 6% per annum up to June 30. [ ICSE Board 2003]

$\begin{array} {|l |l |r |r |r | } \hline \text{Date} & \text{Debit Rs.} & \text{Credit Rs. } & \text{Balance } \\ \hline \text{January 1 } & & 24000.00 & 24000.00 \\ \hline \text{January 20} & 5000.00 & & 19000.00 \\ \hline \text{January 29} & & 10000.00 & 29000.00 \\ \hline \text{March 15} & & 8000.00 & 37000.00 \\ \hline \text{April 3} & & 7653.00 & 44653.00 \\ \hline \text{May 6} & 3040.00 & & 41613,00 \\ \hline \text{May 8} & & 5087.00 & 46700.00 \\ \hline \end{array}$

Answer:

Qualifying principal for various months :

$\begin{array}{|l|c| c| } \hline \text{Month} & \text{Principal (Rs.) } & \text{ Principal correct to nearest multiple of Rs. 10} \\ \hline \text{January } & 19000.00 & 19000.00 \\ \hline \text{February } & 29000.00 & 29000.00 \\ \hline \text{March } & 29000.00 & 29000.00 \\ \hline \text{April } & 44653.00 & 44650.00 \\ \hline \text{May } & 46700 & 46700.00 \\ \hline \text{June } & 46700 & 46700.00 \\ \hline \text{Total } & 215053.00 & 215050.00 \\ \hline \end{array}$

When the principal is not rounded off

$\displaystyle P = \text{ Rs. } 215053.00, \hspace{1.0cm} R = 6\% , \hspace{1.0cm} T = \frac{1}{12} \text{ year }$

$\displaystyle \text{Interest } = \frac{P \times R \times T}{100} = \frac{215053 \times 6 \times 1}{100 \times 12} = \text{ Rs. } 1075.27$

When the principal is taken correct to nearest multiple of Rs. 10

$\displaystyle P = \text{ Rs. } 215050.00, \hspace{1.0cm} R = 6\% , \hspace{1.0cm} T = \frac{1}{12} \text{ year }$

$\displaystyle \text{Interest } = \frac{P \times R \times T}{100} = \frac{215050 \times 6 \times 1}{100 \times 12} = \text{ Rs. } 1075.25$

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Question 8: If the account in question 7 was closed on June 30, calculate the interest.

Answer:

Qualifying principal for various months :

$\begin{array}{|l|c| c| } \hline \text{Month} & \text{Principal (Rs.) } & \text{ Principal correct to nearest multiple of Rs. 10} \\ \hline \text{January } & 19000.00 & 19000.00 \\ \hline \text{February } & 29000.00 & 29000.00 \\ \hline \text{March } & 29000.00 & 29000.00 \\ \hline \text{April } & 44653.00 & 44650.00 \\ \hline \text{May } & 46700 & 46700.00 \\ \hline \text{June } & 0.00 & 0.00 \\ \hline \text{Total } & 168353.00 & 168350.00 \\ \hline \end{array}$

When the principal is not rounded off

$\displaystyle P = \text{ Rs. } 168353.00, \hspace{1.0cm} R = 6\% , \hspace{1.0cm} T = \frac{1}{12} \text{ year }$

$\displaystyle \text{Interest } = \frac{P \times R \times T}{100} = \frac{168353 \times 6 \times 1}{100 \times 12} = \text{ Rs. } 841.77$

When the principal is taken correct to nearest multiple of Rs. 10

$\displaystyle P = \text{ Rs. } 168350.00, \hspace{1.0cm} R = 6\% , \hspace{1.0cm} T = \frac{1}{12} \text{ year }$

$\displaystyle \text{Interest } = \frac{P \times R \times T}{100} = \frac{168350 \times 6 \times 1}{100 \times 12} = \text{ Rs. } 841.75$

$\\$

Question 9: The following table shows a page from the passbook of a bank:

$\begin{array} {|l |l |r |r |r | } \hline \text{Date} & \text{Particulars} & \text{Amount } & \text{Amount } & \text{Balance (Rs.)} \\ & &\text{Withdrawn (Rs.)} & \text{Deposited (Rs.)} & \\ \hline \text{January 1, 03 } & \text{B/F } & & & 2842.00 \\ \hline \text{January 15} & \text{To Self} & 840.00 & & 2002.00 \\ \hline \text{March 6} & \text{By Cash} & & 856.00 & 2858.00 \\ \hline \text{April 10} & \text{To Self} & 1132.00 & & 1726.00 \\ \hline \text{April 25} & \text{By Cheque} & & 638.00 & 2364.00 \\ \hline \text{June 15} & \text{By Cash} & 568.50 & & 1795.50 \\ \hline \end{array}$

Calculate interest from January, 2003 to June, 2003 at 6% pet annum. For every month take the minimum balance (principal) in the nearest multiple of Rs. 10 after 10th day and up to the last day of the month.

Answer:

For finding the principal for every month, prepare a table as shown below:

$\begin{array}{|l|c| c| } \hline \text{Month} & \text{Principal (Rs.) } & \text{ Principal correct to nearest multiple of Rs. 10} \\ \hline \text{January } & 2002.00 & 2000.00 \\ \hline \text{February } & 2002.00 & 2000.00 \\ \hline \text{March } & 2858.00 & 2860.00 \\ \hline \text{April } & 1726.00 & 1730.00 \\ \hline \text{May } & 2364.00 & 2360.00 \\ \hline \text{June } & 1795.50 & 1800.00 \\ \hline \text{Total } & 12747.50 & 12750.00 \\ \hline \end{array}$

$\displaystyle P = \text{ Rs. } 12750.00, \hspace{1.0cm} R = 6\% , \hspace{1.0cm} T = \frac{1}{12} \text{ year }$

$\displaystyle \text{Interest } = \frac{P \times R \times T}{100} = \frac{12750 \times 6 \times 1}{100 \times 12} = \text{ Rs. } 63.75$

$\\$

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.

Answer:

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

$\displaystyle P = \text{ Rs. } 20100, \hspace{1.0cm} I = \text{ Rs. } 83.75 , \hspace{1.0cm} T = \frac{1}{12} \text{ year }$

$\displaystyle \text{Rate } = \frac{I \times 100 }{P \times T } = \frac{83.75 \times 100 \times 12 }{20100 \times 1} = 5\%$

$\\$

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]

Answer:

$\displaystyle P = \text{ Rs. } 200, \hspace{1.0cm} r = 11\% , \hspace{1.0cm} n = 36 \text{ months }$

$\displaystyle \text{Interest } = P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100} = 200 \times \frac{36(36+1)}{2 \times 12} \times \frac{11}{100} = 1221$

Since, the sum deposited $= P \times n = 200 \times 36 = \text{ Rs. } 7200$

Therefore the amount that Kiran will get at the time of maturity $= 7200 + 1221 = \text{ Rs. } 8421$

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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]

Answer:

$\displaystyle P = \text{ Rs. } 80, \hspace{1.0cm} r = 6\% , \hspace{1.0cm} n = 72 \text{ months }$

$\displaystyle \text{Interest } = P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100} = 80 \times \frac{72(72+1)}{2 \times 12} \times \frac{6}{100} = 1051.20$

Since, the sum deposited $= P \times n = 80 \times 72 = \text{ Rs. } 5760$

Therefore the amount that Mohan will get at the time of maturity $= 5760 + 1051.20 = \text{ Rs. } 6811.20$

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Question 13: Ur. 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]

Answer:

$\displaystyle \text{Let } P = \text{ Rs. } x, \hspace{1.0cm} r = 14\% , \hspace{1.0cm} n = 12 \text{ months }$

$\displaystyle \text{Interest } = P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100} = x \times \frac{12(12+1)}{2 \times 12} \times \frac{14}{100} = 0.91x$

Since, the sum deposited $= P \times n = x \times 12 = \text{ Rs. } 12x$

Therefore the amount that Mr. Nair will get at the time of maturity $= 12x + 0.91x = \text{ Rs. } 12.91x$

$\displaystyle \text{Given market value is Rs. } 6455 \Rightarrow 12.91x = 6455 \Rightarrow x = \frac{6455}{12.91} = \text{ Rs. } 500$

$\displaystyle \text{The monthly instalment } =\text{ Rs. } 500$

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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]

Answer:

$\displaystyle \text{(i) Since, 2 years} n = 24 \text{months }$

$\displaystyle \text{Total money deposited in the bank }= 24 \times 2500 = \text{ Rs. } 60000$

$\displaystyle \text{Given; maturity value of the deposit }= \text{ Rs. } 66250$

$\displaystyle \text{The interest paid by the bank = Maturity value - Total sum deposited } \\ \\ = 66250 - 60000 = \text{ Rs. } 6250$

(ii)

$\displaystyle P = \text{ Rs. } 2500, \hspace{1.0cm} I = 6250 , \hspace{1.0cm} n = 24 \text{ months }$

$\displaystyle \text{Interest } = P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100} = 2500 \times \frac{24(24+1)}{2 \times 12} \times \frac{r}{100} = 6250$

$\displaystyle \Rightarrow r = \frac{6250 \times 24 \times 100}{2500 \times 24 \times 25} = 10\%$

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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.

Answer:

Let the account be held for $n$ months

$\displaystyle P = \text{ Rs. } 600, \hspace{1.0cm} r = 10% , \hspace{1.0cm}$

$\displaystyle \text{Interest } = P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100} = 600 \times \frac{n(n+1)}{2 \times 12} \times \frac{10}{100} = \frac{5n(n+1)}{2}$