12

Compound Interest

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
10450.69
B
10455.69
C
10465.69
D
10555.69
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
16527.50
B
16427.50
C
16527.50
D
16537.50
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
There are 15 questions to complete.
12

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