Practice MCQ Questions and Answer on Compound Interest

51.

Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:

(A) Rs. 1550
(B) Rs. 1650
(C) Rs. 1750
(D) Rs. 2000

Solution: $\begin{aligned} C .I . = R s . [4000 \times {(1 + \frac{10}{100})}^{2} - 4000] \\ = R s . (4000 \times \frac{11}{10} \times \frac{11}{10} - 4000) \\ = R s . 840 \\ ∴ Sum = R s . (\frac{420 \times 100}{3 \times 8}) \\ = R s . 1750 \end{aligned}$

52.

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

Solution: $\begin{aligned} Amount = R s . [8000 \times {(1 + \frac{5}{100})}^{2}] \\ = R s . (8000 \times \frac{21}{20} \times \frac{21}{20}) \\ = R s . 8820 \end{aligned}$

53.

Rahul invested equal sums of money at compound interest under two schemes A and B. Under scheme A, the interest rate was 10% per annum and under scheme B, the interest rate was 12% per annum. The compound interest after two years on the sum invested in scheme A was Rs. 1,050. How much is the interest earned under scheme B after two years, if the interest is compounded annually in both schemes?

(A) Rs. 1,722
(B) Rs. 1,270
(C) Rs. 1,272
(D) Rs. 1,372

Solution: $\begin{aligned} CI of A in two years \\ = 10 + 10 + \frac{10 \times 10}{100} \\ = 21 % \\ 21 % \to 1050 \\ 1 % \to 50 \\ 100 % \to Rs . 5000 \\ P = Rs . 5000 \\ CI of B in two years \\ = 12 + 12 + \frac{12 \times 12}{100} \\ = 24 + 1.44 \\ = 25.44 % \\ CI = \frac{5000 \times 25.44}{100} = Rs . 1272 \end{aligned}$

54.

A sum of Rs. 5324 is accumulated in 3 years at 10% compound interest, What is the original amount = ?

(A) Rs. 2000
(B) Rs. 4000
(C) Rs. 6000
(D) Rs. 3000

Solution: Let the principal = 1000, r = 10%, T = 3Year Rate r = 10% = $\frac{1}{10}$ Amount = 300 + 30 + 1 + 1000(Principal) = 1331 ⇒1331 unit → 5324 ⇒ 1unit → $\frac{5324}{1331}$ ∴ 1000unit = $1000 \times \frac{5324}{1331}$ = 4000

55.

The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:

(A) Rs. 400
(B) Rs. 500
(C) Rs. 600
(D) Rs. 800

Solution: $\begin{aligned} Let the sum be Rs. P \\ Then, P {(1 + \frac{10}{100})}^{2} - P = 525 \\ \Rightarrow P [{(\frac{11}{10})}^{2} - 1] = 525 \\ \Rightarrow P = \frac{525 \times 100}{21} = 2500 \\ ∴ Sum = R s . 2500 \\ So, S.I. = R s . (\frac{2500 \times 5 \times 4}{100}) \\ = R s . 500 \end{aligned}$

56.

The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:

(A) 2
(B) $2 \frac{1}{2}$
(C) 3
(D) 4

Solution: $\begin{aligned} Amount = R s . (30000 + 4347) \\ = R s . 34347 \\ Let the time be n years \\ Then, 30000 {(1 + \frac{7}{100})}^{n} = 34347 \\ \Rightarrow {(\frac{107}{100})}^{n} = \frac{34347}{30000} = \frac{11449}{10000} = {(\frac{107}{100})}^{2} \\ ∴ n = 2 years \end{aligned}$

57.

A sum of Rs. x was borrowed and paid back in two equal yearly instalments, each of Rs. 35,280. If the rate of interest was 5%, compounded annually, then the value of x is:

(A) 64,400
(B) 65,600
(C) 64,800
(D) 65,400

58.

A certain sum amount to Rs. 15,500 in 2 years at 12% p.a. simple interest. The same sum will amount to what in $1 \frac{1}{2}$ ÃÂÃÂ years at 10% p.a., if the interest is compounded half yearly (nearest to Rs. 1)?

(A) Rs. 14,470
(B) Rs. 15,125
(C) Rs. 14,360
(D) Rs. 13,460

Solution: $\begin{aligned} 15500 - P = \frac{P \times 12 \times 2}{100} \\ 1550000 - 100 P = 24 P \\ 124 P = 1550000 \\ P = \frac{1550000}{124} \\ P = Rs . 12500 \\ Half yearly, Rate = 5 % \end{aligned}$

59.

The compound interest on a sum of Rs. 20,000 at 15% p.a., for $2 \frac{2}{3}$ ÃÂÃÂ years, interest compounded yearly is:

(A) Rs. 9,098
(B) Rs. 8.896
(C) Rs. 9,000
(D) Rs. 9,095

60.

What is the amount (in Rs.) of a sum of Rs. 32,000 at 20% per annum for 9 months, compounded quarterly?

(A) 37,044
(B) 35,087
(C) 32,000
(D) 30,876

Solution: $\begin{aligned} Principal = Rs . 32000 \\ Rate = 20 % p .a . \\ = \frac{20}{4} % = 5 % quarterly = \frac{1}{20} \\ Time = 9 months = \frac{9}{12} \times 4 = 3 \end{aligned}$ $\begin{matrix} Principal & Amount \\ {(20)}^{3} & : & {(21)}^{3} \\ 8000 & : & 9261 \\ ↓^{\times 4} & ↓^{\times 4} \\ Rs . 32000 & Rs . 37044 \end{matrix}$

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Practice MCQ Questions and Answer on Compound Interest

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