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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]

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Notes: Please refer to quadratic equations for solving this.

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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.

Answer:

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

Answer:

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.

Answer:

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.

Answer:

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]

Answer:

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]

Answer:

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]

Answer:

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]

Answer:

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 \%

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