Question 1:  Given the following details, calculate simple interest at the rate of 6% per annum up to June 30. 

 Date Withdrawals (Rs.) Deposits (Rs.) Balance (Rs.) Jan 1 – 24000 24000 Jan 20 5000 – 19000 Jan 29 – 10000 29000 March 15 8000 37000 April 3 7653 44653 May 6 3040 – 41613 May 8 – 5087 46700

Qualifying principal for various months:

 Month Principal (Rs.) January 19000 February 29000 March 29000 April 44653 May 46700 June 46700 Total 215060 $P = Rs. \ 215060 \ \ R = 6\% \ and \ T= \frac{1}{12}$ $I = P \times R \times T = 215060 \times \frac{6}{100} \times \frac{1}{12} = Rs. \ 1075.27$ $\\$

Question 2: Mr. Ashok has an account in the Central Bank of India. The following entries are from his passbook:-

 Date Particulars Withdrawals (Rs.) Deposits (Rs.) Balance (Rs.) 01.01.05 B/F 1200 07.01.05 By Cash 500 1700 17.01.05 To Cheque 4000 1300 10..02.05 By Cash 800 2100 25.02.05 To Cheque 500 1600 20.09.05 By Cash 700 2300 21.11.05 To Cheque 600 1700 05.12.05 By Cash 300 2000

If Mr. Ashok gets Rs. 83.75 as interest at the end of the year, where the interest rate is compounded annually, calculate the rate of interest paid by the bank in his Savings Bank Account on 31st December 2005. 

Qualifying principal for various months:

 Month Principal (Rs.) January 1300 February 1600 March 1600 April 1600 May 1600 June 1600 July 1600 August 1600 September 1600 October 2300 November 1700 December 2000 Total 20100 $P = Rs. \ 20100 \ \ Rate = r\% \ and \ T= \frac{1}{12} , \ Interest = Rs. \ 83.75$ $I = P \times R \times T$ $83.75= 20100 \times \frac{r}{100} \times \frac{1}{12} \Rightarrow r = 5 \%$ $\\$

Question 3: 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. $P = Rs. \ 200, \ no \ of \ months = 36, \ r = 11\%$ $Maturity \ Value = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $=200 \times 36 +200 \times \frac{36(36+1)}{2 \times 12} \times \frac{11}{100} = Rs. 8421$ $\\$

Question 4: Mohan deposited Rs. 80 per month in a cumulative deposit account for 6 years. Find the amount payable to him on maturity, it the rate of interest is 6% per annum. $P = Rs. \ 80, \ no \ of \ months = 72, \ r = 6\%$ $Maturity \ Value = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $=80 \times 72 +80 \times \frac{72(72+1)}{2 \times 12} \times \frac{6}{100} = Rs. 6811.20$ $\\$

Question 5: 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 installment. $P = Rs. \ x, \ no \ of \ months = 12, \ rate = 14\% \ Maturity Amount = Rs. 6455$ $Maturity \ Value = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $6455 =x \times 12 +x \times \frac{12(12+1)}{2 \times 12} \times \frac{14}{100}$ $x = \frac{6455}{12.91} = Rs. 500$

He must deposit Rs. 500 every month. $\\$

Question 6: 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) interest paid by the bank ii) rate of interest. $P = Rs. \ 2500, \ no \ of \ months = 24, \ rate = r\% \ Maturity Amount = Rs. 66250$ $Maturity \ Value = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $66250 =2500 \times 24 +2500 \times \frac{24(24+1)}{2 \times 12} \times \frac{r}{100} \Rightarrow r=10\%$ $Interest = P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $= 2500 \times \frac{24(24+1)}{2 \times 12} \times \frac{10}{100} = 6250$

Question 7: The entries in a Saving Bank passbook are given below:

 Date Particulars Withdrawals (Rs.) Deposits (Rs.) Balance (Rs.) 01.01.03 B/F 14,00.00 01.02.03 By Cash 11,500.00 25,500.00 12.02.03 To Cheque 5,000 20,500.00 05.04.03 By Cash 3,750.00 24,250.00 15.04.03 To Cheque 4,250.00 20,000.00 09.05.03 By Cash 1,500.00 21,500.00 04.06.03 By Cash 1,500.00 23,000.00

Calculate the interest for six months (January to June) at 4% per Annum on the minimum balance on or after the tenth day of each month. 

Qualifying principal for various months:

 Month Principal (Rs.) January 14000 February 20500 March 20500 April 20000 May 21500 June 23000

Total = Rs. 119500 $P = Rs. \ 119500 \ \ R = 4\% \ and \ T= \frac{1}{12}$ $I = P \times R \times T = 119500 \times \frac{4}{100} \times \frac{1}{12} = Rs. \ 398.33$ $\\$

Question 8: A page from the passbook of Mrs. Rama Bhalla is given below:

 Date Year 2004 Particulars Withdrawals (Rs.) Deposits (Rs.) Balance (Rs.) January 1 B/F 2,000.00 January 9 By Cash 200.00 2,200.00 February 10 To Cheque 500.00 1,700.00 February 24 By Cheque 300.00 2,000.00 July 29 To Cheque 200.00 1,800.00 November 7 By Cash 300.00 2,100.00 December 8 By Cash 200.00 2,300.00

Calculate the interest to Mrs. Rama Bhalla for the period of January 2004 to December 2004, at the rate of 5% per annum. 

Qualifying principal for various months:

 Month Principal (Rs.) January 2200 February 1700 March 2000 April 2000 May 2000 June 2000 July 1800 August 1800 September 1800 October 1800 November 2100 December 2300 Total 23500 $P = Rs. \ 23500 \ \ R = 5\% \ and \ T= \frac{1}{12}$ $I = P \times R \times T = 23500 \times \frac{5}{100} \times \frac{1}{12} = Rs. \ 97.92$ $\\$

Question 9: A page from Saving Bank account of Mr. Prateek is given below:

 Date Particulars Withdrawals (Rs.) Deposits (Rs.) Balance (Rs.) January 1st 2006 B/F – – 1,270 January 7th 2006 By Cheque – 2,310 3,580 March 9th 2006 To Self 2,000 – 1,580 March 26th 2006 By Cash – 6,200 7,780 June 10th 2006 To Cheque 4,500 – 3,280 July 15th 2006 By Clearing – 2,630 5,910 October 18th 2006 To Cheque 530 – 5,380 October 27th 2006 To Self 2,690 – 2,690 November 3rd 2006 By Cash – 1,500 4,190 December 6th 2006 To Cheque 950 – 3,240 December 23rd 2006 By Transfer – 2,920 6,160

If he receives Rs.198 as interest on 1st January 2007. Find the rate of interest paid by the bank. 

Qualifying principal for various months:

 Month Principal (Rs.) January 3580 February 3580 March 1580 April 7780 May 7780 June 3280 July 3280 August 5910 September 5910 October 2690 November 4190 December 3240 Total 52800 $P = Rs. \ 52800 \ \ R = x\% \ and \ T= \frac{1}{12} I = Rs. \ 198$ $I = P \times R \times T \Rightarrow 52800 \times \frac{x}{100} \times \frac{1}{12} = 198 \Rightarrow x = 4.5 \%$ $\\$

Question 10: Mrs. Kapoor opened a Saving Bank Account in State Bank of India on 9th January 2008. Her passbook entries for the year 2008 are given below:

 Date Particulars Withdrawals (Rs.) Deposits (Rs.) Balance (Rs.) Jan. 9, 2008 By Cash – 10,000 10,000 Feb. 12, 2008 By Cash – 15,500 25,500 April 6, 2008 To Cheque 3,500 – 22,000 April 30, 2008 To Self 2,000 – 20,000 July 16, 2008 By Cheque – 6,500 26,500 Aug. 4, 2008 To Self 5,500 – 21,000 Aug. 20, 2008 To Cheque 1,200 – 19,800 Dec. 12, 2008 By Cash – 1,700 21,500

Mrs. Kapoor closed the account on 31st December 2008. If the bank pays interest at 4% per annum, find the interest he receives on closing the account. Give your answer correct to the nearest rupee. 

Answer:  Qualifying principal for various months:

 Month Principal (Rs.) January 10000 February 10000 March 25500 April 20000 May 20000 June 20000 July 20000 August 19800 September 19800 October 19800 November 19800 Total 204700 $P = Rs. \ 204700 \ \ R = 4.0\% \ and \ T= \frac{1}{12}$ $I = P \times R \times T = 204700 \times \frac{4}{100} \times \frac{1}{12} = Rs. \ 682.33 or Rs. 682$ $\\$

Question 11: Explain the following:

i) Punnet has a recurring deposit account in Bank of Baroda and deposits Rs.140 per month for 4 years. If he gets Rs.8,092 on maturity, find the rate of interest given by the bank.

ii) David opened a recurring deposit account in a bank and deposited Rs.300 per month for two years. If he received Rs.7,725 at the time of maturity, find the rate of interest per annum. 

i) $P = Rs. \ 140, \ no \ of \ months = 48, \ rate = r\% \ Maturity Amount = Rs. 8092$ $Maturity \ Value = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $8092 =140 \times 48 +140 \times \frac{48(48+1)}{2 \times 12} \times \frac{r}{100}$ $r = \frac{(8092-140 \times 48) \times (2 \times 12) \times 100}{140 \times 48 \times 49} \Rightarrow r=10\%$

ii) $P = Rs. \ 300, \ no \ of \ months = 24, \ rate = r\% \ Maturity Amount = Rs. 7725$ $Maturity \ Value = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $7725 =300 \times 24 +300 \times \frac{24(24+1)}{2 \times 12} \times \frac{r}{100}$ $r = \frac{(7725-300 \times 24) \times (2 \times 12) \times 100}{300 \times 24 \times 25} \Rightarrow r=7\%$ $\\$

Question 12: Amit deposited 150 per month in a bank for 8 month under the recurring deposit scheme. What will be the maturity value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of every month? [2001, 2007] $P = Rs. \ 150, \ no \ of \ months = 8, \ r = 8\%$ $Maturity \ Value = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $=150 \times 8 +150 \times \frac{8(8+1)}{2 \times 12} \times \frac{8}{100} = Rs. 1236$ $\\$

Question 13: Mr. Gupta opened a recurring deposit account in a bank. He deposited Rs. 2,500 per month for two years. At the time of maturity, he got Rs.67,500. Find:

• The total interest earned by Mr. Gupta
• The rate of interest per annum. $P = Rs. \ 2500, \ no \ of \ months = 24, \ rate = r\% \ Maturity Amount = Rs. 67500$ $Maturity \ Value = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $67500 =2500 \times 24 +2500 \times \frac{24(24+1)}{2 \times 12} \times \frac{r}{100}$ $r = \frac{(67500-2500 \times 24) \times (2 \times 12) \times 100}{2500 \times 24 \times 25} \Rightarrow r=12\%$ $Interest =2500 \times \frac{24(24+1)}{2 \times 12} \times \frac{12}{100} = Rs. \ 7500$ $\\$

Question 14: Given below are the entries in a saving Bank A/C passbook:

 Date Particulars Withdrawals (Rs.) Deposits (Rs.) Balance (Rs.) Feb. 8 B/F – – 8,500 Feb. 18 To Self 4,000 – 4,500 April 12 By Cash – 2,230 6,730 June 15 To Self 5,000 – 1,730 July 8 By Cash – 6,000 7,730

Calculate the interest for six months from February to July at 6% p.a. 

Qualifying principal for various months:

 Month Principal (Rs.) February 4500 March 4500 April 4500 May 6730 June 1730 July 7730 Total 29690 $P = Rs. \ 29690 \ \ R = 6\% \ and \ T= \frac{1}{12}$ $I = P \times R \times T = 29690 \times \frac{6}{100} \times \frac{1}{12} = Rs. \ 148.45$ $\\$

Question 15: Chaudhary opened a saving bank account at State Bank of India on 1st April 2007. The entries of one year as shown in his passbook are given below:

 Date Particulars Withdrawals (Rs.) Deposits (Rs.) Balance (Rs.) 1st April 2007 By Cash – 8,550.00 8,550.00 12th April 2007 To Self 1,200.00 – 7,350.00 24th April 2007 By Cash – 4,550.00 11,900.00 8th July 2007 By Cheque – 1,500.00 13,400.00 10th Sept. 2007 By Cheque – 3,500.00 16,900.00 17th Sept. 2007 To Cheque 2,500.00 – 14,400.00 11th Oct. 2007 By Cash – 800.00 15,200.00 6th Jan. 2008 To Self 2,000.00 – 13,200.00 9th March 2008 By Cheque – 950.00 14,150.00

If the bank pays interest at the rate of 5% per annum, find the interest paid on 1st April 2008. Give your answer correct to nearest rupee. 

Qualifying principal for various months:

 Month Principal (Rs.) April 7350 May 11900 June 11900 July 13400 August 13400 September 14400 October 14400 November 15200 December 15200 January 13200 February 13200 March 14150 Total 157700 $P = Rs. \ 157700 \ \ R = 5\% \ and \ T= \frac{1}{12}$ $I = P \times R \times T = 157700 \times \frac{5}{100} \times \frac{1}{12} = Rs. \ 657.08 or Rs. \ 657$ $\\$

Question 16: Bitto deposits a certain sum of money in a recurring deposit account of a Bank. If the rate of interest of 8% per annum and Mr. Bitto gets Rs.8,008 from the bank after 3 years, find the value of his monthly installment. $P = Rs. \ x, \ no \ of \ months = 36, \ rate = 8\% \ Maturity Amount = Rs. 8008$ $Maturity \ Value = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $8008 =x \times 36 +x \times \frac{36(36+1)}{2 \times 12} \times \frac{8}{100}$ $x = \frac{8008}{40.44} = Rs. 198.02$

He must deposit Rs. 200 every month. $\\$

Question 17: Shahrukh opened a recurring deposit account in a bank and deposited 800 per month for 1 ½ years. If he received Rs.15,084 at the time of maturity. Find the interest rate per annum. $P = Rs. \ 800, \ no \ of \ months = 18, \ rate = r\% \ Maturity Amount = Rs. 15084$ $Maturity \ Value = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $15084 =800 \times 18 +800 \times \frac{18(18+1)}{2 \times 12} \times \frac{r}{100}$ $r = \frac{(15084-800 \times 18) \times (2 \times 12) \times 100}{800 \times 18 \times 19} \Rightarrow r=6\%$ $\\$

Question 18: A page from the saving account of Priyanka is given below:

 Date Particulars Withdrawals (Rs.) Deposits (Rs.) Balance (Rs.) 03/04/2006 B/F 4000.00 05/04/2006 By Cash 2000.00 6000.00 18/04/2006 By Cheque 6000.00 12000.00 25/05/2006 To Cheque 5000.00 7000.00 30/05/2006 By Cash 3000.00 10000.00 20/07/2006 By Self 4000.00 6000.00 10/09/2006 By Cash 2000.00 8000.00 19/09/2006 To Cheque 1000.00 7000.00

If the interest earned by Priyanka for the period ending September 2006 is Rs.175, find the rate of interest. 

Qualifying principal for various months:

 Month Principal (Rs.) April 6000 May 7000 June 10000 July 6000 August 6000 September 7000 Total 42000 $P = Rs. \ 42000 \ \ Rate = r\% \ and \ T= \frac{1}{12} , \ Interest = Rs. \ 175$ $I = P \times R \times T$ $175= 42000 \times \frac{r}{100} \times \frac{1}{12} \Rightarrow r = 5 \%$ $\\$

Question 19: Mr. Dhoni has an account in the Union Bank of India. The following entries are from his passbook:

 Date Particulars Withdrawals (Rs.) Deposits (Rs.) Balance (Rs.) Jan 3, 07 B/F – – 2642.00 Jan 16, 07 To Self 640.00 – 2002.00 March 5, 07 By Cash – 850.00 2852.00 April 10, 07 To Self 1130.00 – 1722.00 April 25, 07 By Check – 650.00 2372.00 June 15, 07 By Cash 577.00 – 1795.00

Calculate the interest from January 2007 to June 2007 at the rate od 4% per annum. 

Qualifying principal for various months:

 Month Principal (Rs.) January 2002 February 2002 March 2852 April 1722 May 2372 June 1795 Total 12745 $P = Rs. \ 12745 \ \ R = 4\% \ and \ T= \frac{1}{12}$ $I = P \times R \times T = 12745 \times \frac{4}{100} \times \frac{1}{12} = Rs. \ 42.48$ $\\$

Question 20: Given below are the entries in a Saving Bank A/c passbook:

 Date Particulars Withdrawals (Rs.) Deposits (Rs.) Balance (Rs.) Feb 8 B/F – – 8500 Feb, 18 To Self 4000 – April, 12 By Cash – 2238 June, 15 To Self 5000 – June, 8 By Cash – 6000

Calculate the interest for the six months, February to July, at 4.5% per annum on the minimum balance on or after the 10th day of each month. [2000, 2007] $P = Rs. \ 29714 \ \ R = 4.5\% \ and \ T= \frac{1}{12}$ $I = P \times R \times T = 29714 \times \frac{4.5}{100} \times \frac{1}{12} = Rs. \ 111.43$ $\\$