Practice MCQ Questions and Answer on Compound Interest

21.

If the compound interest on a sum of money for 3 years at the rate of 5% per annum is Rs. 252.20, the simple interest on the same sum at the same rate and for the same time is ?

(A) Rs. 220
(B) Rs. 240
(C) Rs. 245
(D) Rs. 250

Solution: $\begin{aligned} Rate = 5% \\ Time = 3 years \\ Compound Interest Rs. 252 .20 \\ Effective rate% of CI for 3 years \\ = 15 .7625% \\ Effective rate% of SI for 3 years \\ = 5 \times 3 = 15% \\ Required SI \\ = \frac{252.20}{15.7625} \times 15 \\ = 240 \end{aligned}$

22.

A sum of money put at compound interest amounts in 2 years to Rs. 672 and in 3 years Rs. 714. The rate of interest per annum is = ?

(A) 5.5%
(B) 6.0%
(C) 6.25%
(D) 6.75%

Solution: $\begin{aligned} S .I . on Rs . 672 for 1 year \\ = Rs . (714 - 672) \\ = Rs . 42 \\ ∴ Rate = (\frac{100 \times 42}{672 \times 1}) % \\ = 6 .25% \end{aligned}$

23.

The population of a city in 2014 was 8000000. If in 2015, there is an increment of 8%, in 2016, there is a decrement of 35% and in 2017, there is an increment of 65%, then what is the population of the city at the end of the year 2017?

(A) 8400278
(B) 9266400
(C) 7000000
(D) 9635535

Solution: $\begin{aligned} 8 % = \frac{+ 2}{25}, 35 % = \frac{- 7}{20}, 65 % = \frac{+ 13}{20} \\ 8000000 \times \frac{27}{25} \times \frac{13}{20} \times \frac{33}{20} \\ = 800 \times 27 \times 13 \times 33 \\ = 9266400 Answer \end{aligned}$

24.

A loan of Rs. 12300 at 5% per annum compound interest, is to be repaid in two equal annual installments at the end of every year. Find the amount of each installment ?

(A) Rs. 6651
(B) Rs. 6615
(C) Rs. 6516
(D) Rs. 6156

Solution: $5 % = \frac{1}{20} = \frac{21 \to Installment}{20 \to Principal}$ Year Principal Installment ⇒ I 20×21 → 21×21 ......(i) ⇒ II 400→ 441 .....(ii) Since, installment is equal, hence multiply equation (i) by 21 ⇒ Total principal = 420 + 400 = 820 ⇒ 820 units = Rs. 12300 ⇒ 1 units = Rs. 15 ⇒ 441 units = Rs. 6615 ∴ Each installment = Rs. 6615

25.

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

26.

A person borrowed some money on compound interest and returned it in 3 equal annual instalments. If the rate of interest is 15% per annum and the annual instalment is Rs. 12,167, then find the sum borrowed.

(A) Rs. 27,780
(B) Rs. 28,530
(C) Rs. 25,780
(D) Rs. 26,970

27.

A sum amount to Rs. 7,562 in 4 years and to Rs. 8,469.44 in 5 years at a certain rate percent per annum, when the interest is compounded yearly. The rate of interest is:

(A) 8%
(B) 12%
(C) 20%
(D) 15%

Solution: $\begin{aligned} 7562________8469.44 \\ Rate of interest = \frac{907.44}{7562} \times 100 = 12 % \end{aligned}$

28.

A certain some of money and Rs. 2420 in 2 years and Rs. 2662 in 3 years at same rate of compound interest, compounded annually. The rate of interest per annum is = ?

(A) 6%
(B) 8%
(C) 9%
(D) 10%

Solution: $\begin{aligned} Amount after three years \\ = Rs. 2662 \\ Amount after two years \\ = Rs. 2420 \\ Net interest earned in the 3^{rd} year \\ = 2662 - 2420 \\ = Rs . 242 \\ Rate of interest (r) \\ = \frac{242}{2420} \times 100 = 10% \end{aligned}$ (∴ 2nd year's amount is principal for 3rd year)

29.

What would be the compound interest accrued on an amount of Rs. 8400 @ 12.5 p.c.p.a at the end of 3 years ?

(A) Rs. 2584.16
(B) Rs. 3560.16
(C) Rs. 3820.14
(D) Rs. 4205.62

Solution: $\begin{aligned} Amount \\ = Rs . [8400 \times {(1 + \frac{25}{2 \times 100})}^{3}] \\ = Rs . (8400 \times \frac{9}{8} \times \frac{9}{8} \times \frac{9}{8}) \\ = Rs . (\frac{382725}{32}) \\ = Rs .11960 .156 \approx Rs .11960 .16 \\ C .I . = Rs . (11960.16 - 8400) \\ = Rs . 3560.16 \end{aligned}$

30.

A sum of Rs. 8000 will amount to Rs. 8820 in 2 years if the interest is calculated every year. The rate of compound interest is = ?

(A) 6%
(B) 7%
(C) 3%
(D) 5%

Solution: $\begin{aligned} Principal = Rs 8000 \\ Amount = Rs 8820 \\ Let Rate = R \\ Time = 2 years \\ By using formula, \\ \Rightarrow 8820 = 8000 {(1 + \frac{R}{100})}^{2} \\ \Rightarrow \frac{8820}{8000} = {(1 + \frac{R}{100})}^{2} \\ \Rightarrow \frac{441}{400} = {(1 + \frac{R}{100})}^{2} \\ Taking square root of both sides, \\ \Rightarrow \frac{21}{20} = (1 + \frac{R}{100}) \\ \Rightarrow R = 5 % \end{aligned}$

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Practice MCQ Questions and Answer on Compound Interest

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