Compound Interest

What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly?

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Question: What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly?

[A].

Rs. 2.04

[B].

Rs. 3.06

[C].

Rs. 4.80

[D].

Rs. 8.30

Answer: Option A

Explanation:

C.I. when interest
compounded yearly    
= Rs. 5000 x 1 + 4 x 1 + x 4
100 100
= Rs. 5000 x 26 x 51
25 50
= Rs. 5304.
C.I. when interest is
compounded half-yearly
= Rs. 5000 x 1 + 2 3
100
= Rs. 5000 x 51 x 51 x 51
50 50 50
= Rs. 5306.04

Difference = Rs. (5306.04 – 5304) = Rs. 2.04

A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

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Question: A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

[A].

Rs. 120

[B].

Rs. 121

[C].

Rs. 122

[D].

Rs. 123

Answer: Option B

Explanation:

Amount
= Rs. 1600 x 1 + 5 2 + 1600 x 1 + 5
2 x 100 2 x 100
= Rs. 1600 x 41 x 41 + 1600 x 41
40 40 40
= Rs. 1600 x 41 41 + 1
40 40
= Rs. 1600 x 41 x 81
40 x 40
= Rs. 3321.

C.I. = Rs. (3321 – 3200) = Rs. 121

What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?

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Question:
What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?

[A].

Rs. 9000.30

[B].

Rs. 9720

[C].

Rs. 10123.20

[D].

Rs. 10483.20

Answer: Option C

Explanation:

Amount
= Rs. 25000 x 1 + 12 3
100
= Rs. 25000 x 28 x 28 x 28
25 25 25
= Rs. 35123.20

C.I. = Rs. (35123.20 – 25000) = Rs. 10123.20

Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?

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Question: Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?

[A].

Rs. 8600

[B].

Rs. 8620

[C].

Rs. 8820

[D].

None of these

Answer: Option C

Explanation:

Amount
= Rs. 8000 x 1 + 5 2
100
= Rs. 8000 x 21 x 21
20 20
= Rs. 8820.

Hafeez invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Hafeez at the end of the year will be?

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Hafeez invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Hafeez at the end of the year will be?

A. Rs. 16,500
B. Rs. 16,525.50
C. Rs. 16,537.50
D. Rs. 18,150
Explanation:
P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year = 2 half-year
Amount = [15000 * (1 + 5/100)2]
= (15000 * 21/20 * 21/20) = Rs. 16537.50

A man saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years?

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A man saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years?

A. Rs. 565.25
B. Rs. 635
C. Rs. 662.02
D. Rs. 666.50
Explanation:
Amount = [200(1 + 5/100)3 + 200(1 + 5/100)2 + 200(1 + 5/100)]
= [200 * 21/20(21/20 * 21/20 + 21/20 + 1)] = Rs. 662.02

Shohaib invested Rs. 8000 in a scheme for 2 years at compound interest rate 5% p.a. How much amount will Shohaib get on maturity of the fixed deposit?

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Shohaib invested Rs. 8000 in a scheme for 2 years at compound interest rate 5% p.a. How much amount will Shohaib get on maturity of the fixed deposit?

A. Rs. 8600
B. Rs. 8620
C. Rs. 8800
D. Rs. 8840
E. None of these
Explanation:
Amount = [8000 * (1 + 5/100)2]
= 8000 * 21/20 * 21/20
= Rs. 8820

Afnan wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?

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Afnan wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?

A. Rs.21.60
B. Rs.24.00
C. Rs.25.20
D. Rs.27.80
E. None of these

Rayan invested certain amount for two rates of simple interests at 6% p.a. and 7% p.a. What is the ratio of Rayan’s investments if the interests from those investments are equal?

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Rayan invested certain amount for two rates of simple interests at 6% p.a. and 7% p.a. What is the ratio of Rayan’s investments if the interests from those investments are equal?

A. 4 : 3
B. 3 : 2
C. 6 : 5
D. 7 : 6
E. None of these
Explanation:
Let x be the investment of Rayan in 6% and y be in 7%
x(6)(n)/100 = y(7)(n)/100
=> x/y = 7/6
x : y = 7 : 6