Practice MCQ Questions and Answer on Compound Interest

141.

The difference between CI and SI on a certain sum of money for 3 years at 5% p.a. is Rs. 122. Find the sum invested = ?

(A) Rs. 10000
(B) Rs. 12000
(C) Rs. 16000
(D) Rs. 20000

Solution: $\begin{aligned} Rate of interest = 5 % p .c .p .a . \\ If time 3 years than CI - SI \\ = P [{(\frac{R}{100})}^{3} + 3 {(\frac{R}{100})}^{2}] \\ \Rightarrow 122 = P [{(\frac{5}{100})}^{3} + 3 {(\frac{5}{100})}^{2}] \\ \Rightarrow 122 = P (\frac{125}{1000000} + \frac{75}{10000}) \\ \Rightarrow 122 = P [\frac{125 + 7500}{1000000}] \\ \Rightarrow 122 = P [\frac{7525}{1000000}] \\ \Rightarrow P = \frac{122 \times 1000000}{7625} \\ \Rightarrow P = Rs . 16000 \end{aligned}$

142.

A sum of money doubles itself in 4 years compound interest. It will amount to 8 times itself at the same rate of interest in = ?

(A) 18 years
(B) 12 years
(C) 16 years
(D) 24 years

Solution: $\begin{aligned} Let Principal = P \\ Rate = R% \\ T = 4 years \\ ∴ Amount = 2P \\ Case (I) 2P = P {(1 + \frac{R}{100})}^{4} \\ 2 = {(1 + \frac{R}{100})}^{4} . . . . . (i) \\ Case (II) Let after t years it will be 8 times \\ 8P = P {(1 + \frac{R}{100})}^{t} \\ {(2)}^{3} = {(1 + \frac{R}{100})}^{t} . . . . . (i i) \\ By using equation (i) & equation (ii) \\ {(1 + \frac{R}{100})}^{12} = {(1 + \frac{R}{100})}^{t} \\ By comparing both sides, \\ t = 12 years \end{aligned}$

143.

The compound interest on a sum of Rs. 5,500 at 15% p.a. for 2 years, when the interest is compounded 8 monthly is:

(A) Rs. 1,850
(B) Rs. 1,880
(C) Rs. 1,820.50
(D) Rs. 1,773.75

144.

The compound interest (compounded annually) on a sum of money invested for three years yields Rs. 800 and Rs. 840 in four years. The annual percentage rate of interest is:

(A) 4.5%
(B) 5.5%
(C) 5%
(D) 6%

Solution: Interest of 1 year = 840 - 800 = 40 Rate = $\frac{40}{50}$ × 100 = 5% Answer

145.

How much should you invest today at 10% compound interest annually, to accumulate Rs. 1,61,051 in 5 years?

(A) Rs. 1,11,100
(B) Rs. 1,00,000
(C) Rs. 1,10,000
(D) Rs. 1,11,000

Solution: $\begin{aligned} Rate = 10 % = \frac{1}{10} \\ Time = 5 years \end{aligned}$

146.

The compound interest on Rs 16000 for 9 months at 20% per annum, interest being compounded quarterly, is = ?

(A) Rs. 2520
(B) Rs. 2524
(C) Rs. 2522
(D) Rs. 2518

Solution: The interest is compounded quarterly, $∴ R = \frac{20}{4} = 5 %$ Time = 3 quarters $\begin{aligned} ∴ C . I . = P [{(1 + \frac{R}{100})}^{T} - 1] \\ = 16000 [{(1 + \frac{5}{100})}^{3} - 1] \\ = 16000 [{(\frac{21}{20})}^{3} - 1] \\ = 16000 (\frac{9261 - 8000}{8000}) \\ = 16000 \times \frac{1261}{8000} \\ = Rs . 2522 \end{aligned}$

147.

What will be the compound interest on a sum of Rs. 31,250 for 2 years at 12% p.a., if the interest is compounded 8-monthly

(A) Rs. 8,016
(B) Rs. 8,106
(C) Rs. 8,156
(D) Rs. 8,116

Solution: $\begin{aligned} 12 months \to 12 % \\ 8 months \to 8 % \\ 8 % \to \frac{2}{25} \end{aligned}$

148.

On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum be equal to Rs. 63 ?

(A) Rs. 24600
(B) Rs. 24800
(C) Rs. 25200
(D) Rs. 25500

Solution: $\begin{aligned} Rate of interest = 5 % per annum \\ Time = 2 year \\ Accroding to question, \\ \Rightarrow P [{(1 + \frac{r}{100})}^{n} - 1] - \frac{P \times r \times t}{100} = 63 \\ \Rightarrow P [{(1 + \frac{5}{100})}^{2} - 1] - \frac{P \times 5 \times 2}{100} = 63 \\ \Rightarrow P [{(1 + \frac{5}{100})}^{2} - 1] - \frac{10 P}{100} = 63 \\ \Rightarrow P [{(\frac{105}{100})}^{2} - 1] - \frac{10 P}{100} = 63 \\ \Rightarrow P (\frac{11025 - 10000}{10000}) - \frac{10 P}{100} = 63 \\ \Rightarrow \frac{1025 P}{10000} - \frac{10 P}{100} = 63 \\ \Rightarrow \frac{1025 P - 1000 P}{10000} = 63 \\ \Rightarrow 25 P = R s .630000 \\ \Rightarrow P = \frac{630000}{25} \\ \Rightarrow P = R s . 25200 \\ Hence, sum Rs . 25200 \end{aligned}$

149.

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

150.

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

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Practice MCQ Questions and Answer on Compound Interest

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