Question 1
An amount of Rs.9000 is invested for 2 years at interest rate of 15% per annual and compunded annually. At the end of 2nd year how much amount will be obtained as interest?
 A Rs. 2902.50 B Rs. 2900.50 C Rs. 2899.50 D Rs. 2899
Compound Interest
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Question 1 Explanation:
Amount = P[1+ (R/100)]n
where P = principal, R = rate of interest and n = time(years)
Amount= Rs.9000 x [1 + (15/100)]n = 9000 x (23/20)n = 23805/2 = Rs.11902.5
The amount obtained by the way of interest in compound interest = Amount - principal = Rs.(11902.5 - 9000) = Rs.2902.50
 Question 2
Ram deposits Rs.2000 each on 1st January and 1st July of a year at the rate of 8% compound interest calculated on half-yearly basis. At the end of the year how much amount he would have?
 A Rs.2150.50 B Rs.3182.40 C 4243.20 D 280.40
Compound Interest
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Question 2 Explanation:
We can break this problem into two parts: Rs. 1500 invested for 1 year (Jan to Dec) and Rs. 2000 invested for 6 months (Jul to Dec)
When interest is compounded Half-yearly:
Amount = P[1+ (R/2)/100 ]2n
The total amount for the investment on 1st Jan is: Amount1 = Rs. 2000 x [1+ (8/2)/100]2x1 = Rs. 2000 x [1 + (4/100)]2 = Rs. 2000 x [26/25]2 The total amount for investment on 1st july is: Amount2 = Rs. 2000 x [1+ (8/2)/100][2 x(1/2)] = Rs. 2000 x [1+ 4/100 ] = Rs. 2000 x [26/25] The total amount at the end of the year = amount1 + amount2 = 2000 x [26/25]2 + 2000 x [26/25] = 2000 x [26/25] x [(26/25) + 1] = 2000 x 26/25 x 51/25 = 4243.20
 Question 3
Ram invests Rs. 10,000 for 1 year at a rate of 10% per annum compounded yearly and Sita invests the same amount for same time at same rate per annum compounded half yearly. What is the difference between the interests earned by both?
 A Rs. 25.50 B Rs. 25 C Rs.20.50 D Rs.23.75
Compound Interest
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Question 3 Explanation:
For Ram:
Amount = 10000.[1 + 10/100]1 = Rs.10000 x 11/10 = Rs.11000
For Sita:
Amount= Rs. 10000.[1 +(10/2)/100]2 = 10000 x (21/20)2 = Rs.11025 Difference = Rs.(11000-11025) = Rs.25
 Question 4
Ram has a sum of Rs.8000. He lends it for 20% per annum at compound interest. In how much time the sum of the amount will be Rs.13824?
 A 2 B 1 C 3 D 4
Compound Interest
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Question 4 Explanation:
3824 = 8000 x (1 + 20/100)n
13824/8000 = (120/100)n
(24/20)3 = (12/10)n
(12/10)3 = (12/10)n
=> n = 3 years
 Question 5
Find the amount returned for an investment of Rs.5,000 after 2 years, if the rate of interest for the 1st year is 5% and for the 2nd year is 10%.
 A 772 B 775 C 622 D 820
Compound Interest
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Question 5 Explanation:
Amount = (Principal + Compound interest) = P(1 + R1/100)(1 + R2/100)(1 + R3/100)
Amount = 5000(1 + 5/100)(1 + 10/100)
= 5000 x (21/20)(11/10)
= 5000 x (231/200)
=5775
Interest = 5775 - 5000 = 775
 Question 6
What sum will be amount to Rs.30000 at CI in 3 years, if the rate of interest for 1st, 2nd and 3rd year being 10%, 20% and 30% respectively?
 A 17482.5 B 20145 C 16524 D 17000
Compound Interest
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Question 6 Explanation:
Let Rs.P be the required sum.
30000= p(1 + 10/100)(1 + 20/100)(1 + 30/100)
= p (110/100) x (120/100) x (130/100)
p = 30000x 100 x 100 x 100 / (110 x 120 x 130)
p = 17482.5
 Question 7
What will be the amount if Rs.10,00,000 is invested at CI for 3 years at a rate of interest 10%, 11% and 12% respectively?
 A 1367520 B 1367602 C 1367420 D 1365520
Compound Interest
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Question 7 Explanation:
= p(1 + R1/100)(1 + R2/100)(1 + R3/100)
= 10,00,000 x(1 + 10/100)x(1 + 11/100)x(1 + 12/100)
= 10,00,000 x (110/100) x (111/100) x (112/100)
= 110 x 111 x 112
 Question 8
An amount of Rs.9600 lent out at a rate of 4.5 % per annum for a 1 year and 9 months. At the end of the period, the amount he earned as C.I was:
 A 10450.7 B 10455.7 C 10465.7 D 10555.7
Compound Interest
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Question 8 Explanation:
Amount = 9600 * (1+4.5/100)7/4
= 9600*(104.5/100)7/4
=10455.69
 Question 9
An amount of Rs.8000 is landed out for 2 years at compound interest rate 5 % per annum. How much interest will be incurred on maturity of the FD?
 A 850 B 832 C 800 D 820
Compound Interest
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Question 9 Explanation:
= 8000(1+5/100)2 – 8000
= 8000(105/100)2 – 8000
= 8000 [(105/100)2 -1]
= 8000 [1.1025-1]
= 8000 X 0.1025
= 820
 Question 10
An amount of Rs.15,000 is invested at 10% per annum for one year. If the interest is compounded half-yearly, then what amount will be received at the end of the year?
 A 16527.5 B 16427.5 C 16527.5 D 16537.5
Compound Interest
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Question 10 Explanation:
A= 15000 [1+(10/2)/100]2
= 15000 [105/100]2
= 15000 X 1.1025
= 16537.50
 Question 11
Find the compound interest on Rs. 15,000 for 9 months at 16% per annum compounded quarterly.
 A 1872.96 B 1972.96 C 2072.96 D 2172.96
Compound Interest
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Question 11 Explanation:
CI = 15000[1+(16/4)/100]4X(9/12) -15000
= 15000[104/100]3 - 15000
= 15000 [1.125-1]
= 15000 X 0.125
= 1872.96
 Question 12
An amount of 200000 is deposited in bank under a scheme which provides 10% rate 1st years, 20% rate 2nd year and 5% rate 3rd year. After 3rd year what amount will be returned?
 A 277400 B 277220 C 277200 D 277320
Compound Interest
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Question 12 Explanation:
A = 200000 (1+10/100)(1+20/100)(1+5/100)
A= 200000(110/100)(120/100)(105/100)
A= 277200
 Question 13
A sum of money is borrowed and paid back in two annual installments of Rs. 882 each allowing 5% compound interest. The sum borrowed was:
 A 1540 B 1640 C 1580 D 1680
Compound Interest
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Question 13 Explanation:
Principal = Present worth of the installment at the end of first year + Present worth of the installment at the end of second year = 882/(1 + 5%) + 882/(1 + 5%)^2 = 882/(1 + 5/100) + 882/(1 + 5/100)^2 = 882/(105/100) + 882/(105/100)^2 = 882/(21/20) + 882/(21/20)^2 = 882*20/21 + 882*400/441 = 42*20 + 2*400 = 840 + 800 = 1640.
 Question 14
The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:
 A 6 B 4 C 5 D 3
Compound Interest
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Question 14 Explanation:
Let the Principal be P. Then, P(1 + 20%)^n > 2P Or, P(1 + 1/5)^n > 2P Or, P(6/5)^n > 2P Or (6/5)^n > 2. Now, (6/5)^3 = 1.728 (6/5)^4 = 2.074 Therefore, in 4 years.
 Question 15
The difference between compound interest and simple interest on an amount of Rs 15,000 for 2 years is Rs 96. What is the rate of interest per annum?
 A 8 B 9 C 10 D None of these
Compound Interest
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Question 15 Explanation:
Simple Interest = 15000 * R/100 * 2 Compound Interest = 15000 * (1 + R/100)^2 - 15000 We have, [ 15000 * (1 + R/100)^2 - 15000 ] - [15000 * R/100 * 2] = 96 15000 [ (1 + R/100)^2 - 1 - 2R/100 ] = 96 15000 [ 1 + R^2/10000 + 2R/100 - 1 - 2R/100 ] = 96 15000 [ R^2/10000 ] = 96 R^2 = 96 * 10000/15000 = 96 * 2/3 = 64 R = 8.
There are 15 questions to complete.

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