Practice MCQ Questions and Answer on Compound Interest

151.

The compound interest on a certain sum of money for 2 years at 5% is Rs. 328, then the sum is = ?

(A) Rs. 3000
(B) Rs. 3600
(C) Rs. 3200
(D) Rs. 3400

152.

The compound interest on a certain sum of money at 5% per annum for 2 years is Rs 246. The simple interest on the same sum for 3 years at 6% per annum is = ?

(A) Rs. 435
(B) Rs. 450
(C) Rs. 430
(D) Rs. 432

Solution: $\begin{aligned} Effective rate of CI for 2 years \\ = 5 + 5 + \frac{5 \times 5}{100} \\ = 10.25 % \\ Effective rate of SI for 3 years \\ = 6 \times 3 = 18% \\ According to question \\ Required SI \\ = \frac{246}{10.25} \times 18 \\ = Rs. 432 \end{aligned}$

153.

What will be the difference between S.I. and C.I. on a sum of Rs. 15000 for 2 years at the same rate of interest of $12 \frac{1}{2}$ % per annum ?

(A) Rs. 230.550
(B) Rs. 234.375
(C) Rs. 250.129
(D) Rs. 324.357

Solution: $\begin{aligned} S .I . = Rs . (15000 \times \frac{25}{2} \times 2 \times \frac{1}{100}) \\ = Rs . 3750 \\ C .I . = Rs . [15000 {(1 + \frac{25}{2 \times 100})}^{2} - 15000] \\ = Rs . (15000 \times \frac{9}{8} \times \frac{9}{8} - 15000) \\ = Rs . (18948.375 - 15000) \\ = Rs . 3984.375 \\ Difference \\ = Rs . (3984.375 - 3750) \\ = Rs . 234.375 \end{aligned}$

154.

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

Solution: $\begin{aligned} = Rs . [1600 \times {(1 + \frac{5}{2 \times 100})}^{2} + 1600 \times (1 + \frac{5}{2 \times 100})] \\ = Rs . [1600 \times \frac{41}{40} \times \frac{41}{40} + 1600 \times \frac{41}{40}] \\ = Rs . [1600 \times \frac{41}{40} (\frac{41}{40} + 1)] \\ = Rs . (\frac{1600 \times 41 \times 81}{40 \times 40}) \\ = Rs . 3321 \\ ∴ C .I . = Rs . (3321 - 3200) \\ = Rs . 121 \end{aligned}$

155.

A man invests Rs 4000 for 3 years at compound interest. After one year the money amounts to Rs. 4320. What will be the amount (to the nearest rupee) due at the end of 3 years ?

(A) Rs. 4939
(B) Rs. 5039
(C) Rs. 5789
(D) Rs. 6129

Solution: $\begin{aligned} Le the rate be R % p .a . \\ Then, \\ 4000 (1 + \frac{R}{100}) = 4320 \\ \Rightarrow 1 + \frac{R}{100} = \frac{4320}{4000} = \frac{108}{100} \\ \Rightarrow \frac{R}{100} = \frac{8}{100} \\ \Rightarrow R = 8 \\ ∴ Amount after 3 yeras \\ = Rs . [4000 + {(1 + \frac{8}{100})}^{3}] \\ = Rs . (4000 \times \frac{27}{25} \times \frac{27}{25} \times \frac{27}{25}) \\ = Rs . (\frac{629856}{125}) \\ = Rs . 5038.848 \approx 5039 \end{aligned}$

156.

An amount of Rs. 10000 becomes Rs. 14641 in 2 years if the interest is compounded half yearly. What is the rate of compound interest p.c.p.a. ?

(A) 10%
(B) 12%
(C) 16%
(D) 20%

Solution: $\begin{aligned} Let the rate be R% p .a . \\ Then, \\ 10000 {(1 + \frac{R}{2 \times 100})}^{4} = 14641 \\ \Rightarrow {(1 + \frac{R}{200})}^{4} = \frac{14641}{10000} = {(\frac{11}{10})}^{4} \\ \Rightarrow 1 + \frac{R}{200} = \frac{11}{10} \\ \Rightarrow \frac{R}{200} = \frac{1}{10} \\ \Rightarrow R = 20% \end{aligned}$

157.

A sum of money after a period of 2 years becomes Rs. 34,560, and it becomes Rs. 41,472 after a period of three years, being compounded at 'R' rate of interest. What is the value of R?

(A) 20%
(B) 12%
(C) 25%
(D) 10%

Solution: $\begin{aligned} CI of 1 year = 41472 - 34560 = 6912 \\ Rate % = \frac{6912}{34560} \times 100 \\ = 2 \times 10 \\ = 20 % Answer \end{aligned}$

158.

The compound interest on a certain sum of money at a certain rate for 2 years is Rs. 40.80 and the simple interest on the same sum is Rs. 40 at the same rate and for the same time. The rate of interest is = ?

(A) 2% per annum
(B) 3% per annum
(C) 4% per annum
(D) 5% per annum

Solution: Difference in CI and SI for 2 years $\begin{aligned} = (40.80 - 40) \\ = Rs 0 .80 \\ SI for first year \\ = \frac{40}{2} = Rs . 20 \\ Required Rate % \\ = \frac{0.80}{20} \times 100 = 4 % \end{aligned}$

159.

A certain amount money at R% compounded annually after two and three years becomes Rs. 1440 and Rs. 1728 respectively, R% is ?

(A) 5%
(B) 10%
(C) 15%
(D) 20%

Solution: Here, b – a = 3 – 2 = 1 B = Rs. 1728, A = Rs.1440 $\begin{aligned} R % = (\frac{B}{A} - 1 \times 100) % \\ = (\frac{1728}{1440} - 1 \times 100) % \\ = (\frac{288}{1440} \times 100) % \\ = 20 % \end{aligned}$

160.

If the difference between the compound interest and simple interest on a certain sum at the rate of 5% per annum for 2 years is Rs. 20, then the sum is = ?

(A) Rs. 2000
(B) Rs. 4000
(C) Rs. 6000
(D) Rs. 8000

Solution: Let the sum be = 400x Simple Interest = $\frac{P T R}{100}$ S.I = $\frac{400 x \times 2 \times 5}{100}$ = 40x for Compond Interest 5% = $\frac{1}{20}$ C.I = 20x + 20x + x = 41x Difference = 41x - 40x = 20 i.e. x = 20 ∴ Sum is = 400 × 20 = 8000

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Practice MCQ Questions and Answer on Compound Interest

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