Question 1: 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 $\displaystyle P = \text{ Rs. } 29690 R = 6\% \text{ and } T= \frac{1}{12}$ $\displaystyle I = P \times R \times T = 29690 \times \frac{6}{100} \times \frac{1}{12} = \text{ Rs. } 148.45$ $\\$

Question 2: A page from a passbook of saving bank account is given below:

 Date Particulars Withdrawals (Rs.) Deposits (Rs.) Balance (Rs.) 09.08.1999 By Cash – 10,000 10,000 11.08.1999 By Cheque – 5,000 15,000 05.10.1999 To Cheque 12,000 – 3,000 10.10.1999 By Cash – 17,000 20,000 27.11.1999 By Cheque 5,000 – 15,000 29.11.1999 By Cash – 3,000 18,000

The account is closed on 2nd January 2000. Find the amount received, if the rate of interest is 5% p.a.

Qualifying principal for various months:

 Month Principal (Rs.) August 10000 September 15000 October 20000 November 15000 December 18000 January 0 Total 78000 $\displaystyle P = \text{ Rs. } 78000 R = 5\% \text{ and } T= \frac{1}{12}$ $\displaystyle I = P \times R \times T = 78000 \times \frac{5}{100} \times \frac{1}{12} = \text{ Rs. } \ 325$

Amount received $\displaystyle = 18000+325 = \text{ Rs. } \ 18325$ $\\$

Question 3: A person had a Account in Bank. His passbook had the following entries:

 Date Particulars Withdrawals (Rs.) Deposits (Rs.) Balance (Rs.) Jan. 1, 2000 By Balance – – 9,600 Jan. 8 By Cash – 6,000 15,600 Feb. 18 To Cheque 10,500 – 5,100 May 19 By Cash – 6,300 11,400 July 15 By Self 2,400 – 9,000 Oct. 7 By Cash – 3,600 12,000

On October 30th, 2000, he closed the account. If the amount of interest he received on closing account on 30th Oct. 2000 is Rs.310; Calculate the rate of interest per annum.

Qualifying principal for various months:

 Month Principal (Rs.) January 15600 February 5100 March 5100 April 5100 May 5100 June 11400 July 9000 August 9000 September 9000 October 12000 Total 86400 $\displaystyle P = \text{ Rs. } \ 86400 \text{, Rate } = r\% \ and \ T= \frac{1}{12} , \ Interest = \text{ Rs. } \ 310$ $\displaystyle I = P \times R \times T$ $\displaystyle 310= 86400 \times \frac{r}{100} \times \frac{1}{12} \Rightarrow r = 4.31 \%$ $\displaystyle \\$

Question 4: A person deposited 600 per month in a recurring deposit account for 4 years. If the rate of interest is 8% per year; calculate the maturity value of his account. $\displaystyle P = \text{ Rs. } \ 600$, no of months $\displaystyle = 48, \ r = 8\%$ $\displaystyle \text{Maturity Value } = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $\displaystyle =600 \times 48 +600 \times \frac{48(48+1)}{2 \times 12} \times \frac{8}{100} = \text{ Rs. } 33504$ $\displaystyle \\$

Question 5: A person has a recurring deposit account in a bank and deposits 80 per month for 18 months. Find the rate of interest paid by the bank if the maturity value of this account is Rs.1,554. $\displaystyle P = \text{ Rs. } \ 80$, no of months $\displaystyle = 18 \text{, Rate } = r\%$ Maturity Amount $\displaystyle = \text{ Rs. } 1554$ $\displaystyle \text{Maturity Value } = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $\displaystyle 1554 =80 \times 18 +80 \times \frac{18(18+1)}{2 \times 12} \times \frac{r}{100}$ $\displaystyle r = \frac{(1554-80 \times 18) \times (2 \times 12) \times 100}{80 \times 18 \times 19} \Rightarrow r=10\%$ $\displaystyle \\$

Question 6: The maturity value of recurring deposit account is 16,176. If the monthly installment is Rs.400 and the rate of interest is 8% find the time of this Account. $\displaystyle P = \text{ Rs. } \ 400$, no of months $\displaystyle = n \text{, Rate } = 8\%$ Maturity Amount $\displaystyle = \text{ Rs. } 16176$ $\displaystyle \text{Maturity Value } = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $\displaystyle 16176 =400 \times n +400 \times \frac{n(n+1)}{2 \times 12} \times \frac{8}{100}$ $\displaystyle 16176 = 400n + \frac{4}{3} n(n+1)$ $\displaystyle \text{or } n^2+301n-12132=0 \Rightarrow n = 36 \ or -337$

Hence n = 36 months. $\displaystyle \\$

Question 7: A person needs Rs.30,000 after 2 years. What least money (in multiple of Rs.5) must he deposit every month in Recurring Deposit account to get required money after 2 years, the rate of interest being 8% p.a. $\displaystyle P = \text{ Rs. } \ x$, no of months $\displaystyle = 24 \text{, Rate } = 8\%$ Maturity Amount $\displaystyle = \text{ Rs. } 30000$ $\displaystyle \text{Maturity Value } = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $\displaystyle 30000 =x \times 24 +x \times \frac{24(24+1)}{2 \times 12} \times \frac{8}{100}$ $\displaystyle x = \frac{30000}{26} = \text{ Rs. } 1153.84$

He must deposit Rs. 1155 every month. $\displaystyle \\$

Question 8: A person has a recurring deposit account in a bank for 3 years at 8% p.a. simple interest. If he gets 9,990 as interest at the time of maturity, find

• The monthly installment.
• The amount of maturity $\displaystyle P = \text{ Rs. } \ x$, no of months $\displaystyle = 36 \text{, Rate } = 8\%$ Interest Amount $\displaystyle = \text{ Rs. } 9990$ $\displaystyle \text{Interest Value } = P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $\displaystyle 9990 =x \times \frac{36(36+1)}{2 \times 12} \times \frac{8}{100}$ $\displaystyle x = \frac{9990}{4.44} = \text{ Rs. } 2250$ $\displaystyle \text{Maturity Value } = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $\displaystyle =2250 \times 36 +2250 \times \frac{36(36+1)}{2 \times 12} \times \frac{8}{100} = \text{ Rs. } 90990$ $\displaystyle \\$

Question 9: A person has cumulative recurring deposit account and deposits 900 per month for a period of 4 years, if he gets Rs.52,020 at the time of maturity, find the rate of interest. $\displaystyle P = \text{ Rs. } \ 900$, no of months $\displaystyle = 48 \text{, Rate } = r\%$ Maturity Amount $\displaystyle = \text{ Rs. } 52020$ $\displaystyle \text{Maturity Value } = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $\displaystyle 52020 =900 \times 48 +900 \times \frac{48(48+1)}{2 \times 12} \times \frac{r}{100}$ $\displaystyle r = \frac{(52020-900 \times 48) \times (2 \times 12) \times 100}{900 \times 48 \times 49} \Rightarrow r=10\%$ $\displaystyle \\$

Question 10: A person has a 4 year recurring deposit account in a bank and deposits 1,800 per month. If she gets Rs.1,08,450 at the time of maturity, find the rate of interest. $\displaystyle P = \text{ Rs. } \ 1800$, no of months $\displaystyle = 48 \text{, Rate } = r\%$ Maturity Amount $\displaystyle = \text{ Rs. } 108450$ $\displaystyle \text{Maturity Value } = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $\displaystyle 108540 =1800 \times 48 +1800 \times \frac{48(48+1)}{2 \times 12} \times \frac{r}{100}$ $\displaystyle r = \frac{(108450-1800 \times 48) \times (2 \times 12) \times 100}{1800 \times 48 \times 49} \Rightarrow r=12.5\%$ $\displaystyle \\$

Question 11: 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 $\displaystyle P = Rs. \ 157700 R = 5\% \ and \ T= \frac{1}{12}$ $\displaystyle I = P \times R \times T = 157700 \times \frac{5}{100} \times \frac{1}{12} = Rs. \ 657.08 or Rs. \ 657$ $\\$

Question 12: 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. $\displaystyle P = Rs. \ x$, no of months $\displaystyle = 36$ , Rate $\displaystyle = 8\%$ Maturity Amount $\displaystyle = Rs. 8008$ $\displaystyle \text{Maturity Value } = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $\displaystyle 8008 =x \times 36 +x \times \frac{36(36+1)}{2 \times 12} \times \frac{8}{100}$ $\displaystyle x = \frac{8008}{40.44} = Rs. 198.02$

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

Question 13: 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. $\displaystyle P = Rs. \ 800$, no of months $\displaystyle = 18$ , Rate $\displaystyle = r\%$ Maturity Amount $\displaystyle = Rs. 15084$ $\displaystyle \text{Maturity Value } = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$ $\displaystyle 15084 =800 \times 18 +800 \times \frac{18(18+1)}{2 \times 12} \times \frac{r}{100}$ $\displaystyle r = \frac{(15084-800 \times 18) \times (2 \times 12) \times 100}{800 \times 18 \times 19} \Rightarrow r=6\%$ $\displaystyle \\$

Question 14: 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. $\displaystyle P = \text{ Rs. } 42000 \text{ Rate } = r\% \text{ and } T= \frac{1}{12} \text{ , Interest } = Rs. 175$ $\displaystyle I = P \times R \times T$ $\displaystyle 175= 42000 \times \frac{r}{100} \times \frac{1}{12} \Rightarrow r = 5 \%$ $\\$