Practice MCQ Questions and Answer on Compound Interest

111.

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

112.

The compound interest on Rs. 4000 for 4 years at 10% per annum will be = ?

(A) Rs. 1856.40
(B) Rs. 1600
(C) Rs. 1856
(D) Rs. 1756.60

Solution: $\begin{aligned} 10 % = \frac{1}{10} \\ Principal Amount \\ 10 11 \\ 10 11 \\ 10 11 \\ 10 11 \\ \underset{CI = 4641}{\underset{⏟}{\overset{―}{10000 : 14641}}} \\ ∵ Principal = 10000 units \\ = Rs . 4000 (given) \\ 1 unit = \frac{2}{5} \\ CI = 4641 unit \\ = Rs . (\frac{2}{5} \times 4641) \\ = Rs . 1856.40 \end{aligned}$

113.

A sum of Rs. 4,620 is to be paid back in 2 equal annual instalments. How much is each instalments (in Rs.) if the interest is compounded annually at 10% per annum?

(A) 2,420
(B) 2,552
(C) 2,662
(D) 2,750

Solution: $\begin{aligned} P = Rs . 4620 \\ R = 10 % = \frac{1}{10} \end{aligned}$ $\begin{matrix} Principal & Instalments \\ 110 = 10 \times 11 & 11 \times 11 = 121 \\ 100 = 100 & 121 \\ \begin{matrix} 210 \\ ↓^{\times 22} \end{matrix} & \begin{matrix} ↓^{\times 22} \end{matrix} \\ 4620 & Rs . 2662 \end{matrix}$

114.

The compound interest on Rs. 6000 at 10% per annum for $1 \frac{1}{2}$ years, when the interest being compounded annually, is = ?

(A) Rs. 910
(B) Rs. 870
(C) Rs. 930
(D) Rs. 900

Solution: $\begin{aligned} Principal = Rs 6000 \\ Rate % = 10 % \\ Time (t) = 1 \frac{1}{2} years \end{aligned}$ $\begin{aligned} 2^{nd} year CI = 660 \\ 6 months 2^{nd} year CI \\ = \frac{660}{2} = 330 \\ Total CI \\ = (600 + 330) \\ = 930 \end{aligned}$

115.

The sum of money which when given on compound interest at 18% per annum would fetch Rs 960 more when the interest is payable half-yearly then when it was payable annually for 2 years is = ?

(A) Rs. 60000
(B) Rs. 30000
(C) Rs. 40000
(D) Rs. 50000

Solution: Rate of interest = 18% Time = 2 year When the interest is payable half yearly Then, rate of interest = 9% Time = 4 half - years Let the principal be Rs. x $\begin{aligned} C .I . = x [{(1 + \frac{R}{100})}^{T} - 1] \\ = x [{(1 + \frac{9}{100})}^{4} - 1] \\ = x [{(\frac{109}{100})}^{4} - 1] \\ = x [1.4116 - 1] \\ = R s . 0.4116 x \\ According to question \\ = x [{(1 + \frac{18}{100})}^{2} - 1] \\ = x [{(\frac{118}{100})}^{2} - 1] \\ = x [{(1.18)}^{2} - 1] \\ = x [1.3924 - 1] \\ = R s . 0.3924 x \\ According to question, \\ 0.4116 x - 0.3924 x = 960 \\ \Rightarrow x = \frac{960}{0.0192} \\ \Rightarrow x = \frac{960 \times 10000}{192} \\ \Rightarrow x = 50000 \\ Hence, sum of money \\ = Rs. 50000 \end{aligned}$

116.

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

117.

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

118.

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

119.

The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:

(A) 6.06%
(B) 6.07%
(C) 6.08%
(D) 6.09%

Solution: $\begin{aligned} Amount of Rs . 100 for 1 year when \\ compounded half - yearly \\ = R s . [100 \times {(1 + \frac{3}{100})}^{2}] \\ = R s . 106.09 \\ ∴ Effective rate = (106.09 - 100) % \\ = 6.09 % \end{aligned}$

120.

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 $\begin{aligned} ∴ C . I . = P [{(1 + \frac{R}{100})}^{T} - 1] \\ = 16000 [{(1 + \frac{5}{100})}^{3} - 1] \\ = 16000 [{(\frac{21}{20})}^{3} - 1] \\ = 16000 (\frac{9261 - 8000}{8000}) \\ = 16000 \times \frac{1261}{8000} \\ = Rs . 2522 \end{aligned}$

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Practice MCQ Questions and Answer on Compound Interest

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