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. [2013]

Qualifying principal for various months:

 Month Principal (Rs.) February 4500 March 4500 April 4500 May 6730 June 1730 July 7730 Total 29690

$P = Rs. \ 29690 R = 6\% \ and \ T=$ $\frac{1}{12}$

$I = P \times R \times T = 29690 \times$ $\frac{6}{100}$ $\times$ $\frac{1}{12}$ $= Rs. \ 148.45$

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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

$P = Rs. \ 78000 R = 5\% \ and \ T=$ $\frac{1}{12}$

$I = P \times R \times T = 78000 \times$ $\frac{5}{100}$ $\times$ $\frac{1}{12}$ $= Rs. \ 325$

Amount received $= 18000+325 = Rs. \ 18325$

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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

$P = Rs. \ 86400$ , Rate $= r\% \ and \ T=$ $\frac{1}{12}$ $, \ Interest = Rs. \ 310$

$I = P \times R \times T$

$310= 86400 \times$ $\frac{r}{100}$ $\times$ $\frac{1}{12}$ $\Rightarrow r = 4.31 \%$

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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.

$P = Rs. \ 600$, no of months $= 48, \ r = 8\%$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$=600 \times 48 +600 \times$ $\frac{48(48+1)}{2 \times 12}$ $\times$ $\frac{8}{100}$ $= Rs. 33504$

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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.

$P = Rs. \ 80$, no of months $= 18$ , Rate $= r\%$ Maturity Amount $= Rs. 1554$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$1554 =80 \times 18 +80 \times$ $\frac{18(18+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$r =$ $\frac{(1554-80 \times 18) \times (2 \times 12) \times 100}{80 \times 18 \times 19}$ $\Rightarrow r=10\%$

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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.

$P = Rs. \ 400$, no of months $= n$ , Rate $= 8\%$ Maturity Amount $= Rs. 16176$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$16176 =400 \times n +400 \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{8}{100}$

$16176 = 400n +$ $\frac{4}{3}$ $n(n+1)$

or $n^2+301n-12132=0 \Rightarrow n = 36 \ or -337$

Hence n = 36 months.

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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.

$P = Rs. \ x$, no of months $= 24$ , Rate $= 8\%$ Maturity Amount $= Rs. 30000$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$30000 =x \times 24 +x \times$ $\frac{24(24+1)}{2 \times 12}$ $\times$ $\frac{8}{100}$

$x =$ $\frac{30000}{26}$ $= Rs. 1153.84$

He must deposit Rs. 1155 every month.

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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

$P = Rs. \ x$, no of months $= 36$ , Rate $= 8\%$ Interest Amount $= Rs. 9990$

Interest Value $= P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$9990 =x \times$ $\frac{36(36+1)}{2 \times 12}$ $\times$ $\frac{8}{100}$

$x = \frac{9990}{4.44}$ $= Rs. 2250$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$=2250 \times 36 +2250 \times$ $\frac{36(36+1)}{2 \times 12}$ $\times$ $\frac{8}{100}$ $= Rs. 90990$

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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.

$P = Rs. \ 900$, no of months $= 48$ , rate $= r\%$ Maturity Amount $= Rs. 52020$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$52020 =900 \times 48 +900 \times$ $\frac{48(48+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$r =$ $\frac{(52020-900 \times 48) \times (2 \times 12) \times 100}{900 \times 48 \times 49}$ $\Rightarrow r=10\%$

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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.

$P = Rs. \ 1800$, no of months $= 48$ , Rate $= r\%$ Maturity Amount $= Rs. 108450$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$108540 =1800 \times 48 +1800 \times$ $\frac{48(48+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$r =$ $\frac{(108450-1800 \times 48) \times (2 \times 12) \times 100}{1800 \times 48 \times 49}$ $\Rightarrow r=12.5\%$

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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. [2011]

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

$P = Rs. \ 157700 R = 5\% \ and \ T=$ $\frac{1}{12}$

$I = P \times R \times T = 157700 \times$ $\frac{5}{100}$ $\times$ $\frac{1}{12}$ $= Rs. \ 657.08 or Rs. \ 657$

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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. [2013]

$P = Rs. \ x$, 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.

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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. [2014]

$P = Rs. \ 800$, no of months $= 18$ , Rate $= r\%$ Maturity Amount $= Rs. 15084$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$15084 =800 \times 18 +800 \times$ $\frac{18(18+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$r =$ $\frac{(15084-800 \times 18) \times (2 \times 12) \times 100}{800 \times 18 \times 19}$ $\Rightarrow r=6\%$

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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. [2014]

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