Practice MCQ Questions and Answer on Compound Interest

141.

A sum becomes Rs. 2916 in 2 years at 8% per annum compound interest. The simple interest at 9% per annum for 3 years on the same amount will be = ?

(A) Rs. 600
(B) Rs. 675
(C) Rs. 650
(D) Rs. 625

Solution: $\begin{aligned} Amount = Rs . 2916 \\ Time = 2 years \\ Rate = 8 % \\ Effective rate % CI for 2 years \\ = 8 + 8 + \frac{8 \times 8}{100} = 16.64 % \\ Required sum \\ = \frac{2916}{(100 + 16.64)} \times 100 \\ = Rs . 2500 \\ Required simple interest \\ = \frac{2500 \times 9 \times 3}{100} \\ = Rs . 675 \end{aligned}$

142.

The compound interest on Rs. 5000 for 3 years at 10% p.a. will amount to = ?

(A) Rs. 1654
(B) Rs. 1655
(C) Rs. 1600
(D) Rs. 1565

Solution: $\begin{aligned} Principal = Rs. 5000 \\ Time = 3 years \\ Rate = 10 % = \frac{1}{10} \\ Principal Amount \\ 10 11 \\ 10 11 \\ 10 11 \\ \underset{331 units}{\underset{⏟}{\overset{―}{1000 1331}}} \\ \Rightarrow 1000 units = Rs 5000 \\ \Rightarrow 1 units = Rs 5 \\ \Rightarrow 331 units = 331 \times 5 \\ = Rs. 1655 \end{aligned}$

143.

In how many years will a sum of Rs. 800 at 10% per annum compounded semi annually become Rs. 926.10?

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

Solution: $\begin{aligned} Let the time be n year \\ Then, \\ 800 \times {(1 + \frac{5}{100})}^{2 n} = 926.10 \\ \Leftrightarrow {(1 + \frac{5}{100})}^{2 n} = \frac{9261}{8000} \\ \Leftrightarrow {(\frac{21}{20})}^{2 n} = {(\frac{21}{20})}^{3} \\ \Leftrightarrow 2 n = 3 \\ \Leftrightarrow n = \frac{3}{2} \\ ∴ n = 1 \frac{1}{2} years \end{aligned}$

144.

What is the difference (in Rs.) between the interests on Rs. 50,000 for one year at 8% per annum compounded half yearly and yearly?

(A) 80
(B) 50
(C) 70
(D) 100

Solution: $\begin{aligned} 1 year CI = 1 year SI \\ SI = \frac{P \times R \times T}{100} \\ = \frac{50000 \times 8 \times 1}{100} \\ = 4000 \\ Compound interest at half yearly \\ Rate = \frac{8}{2} = 4 % \\ Time = 1 \times 2 = 2 years \\ A = P {(1 + \frac{R}{100})}^{n} \\ A = 50000 {(1 + \frac{4}{100})}^{2} \\ A = 50000 \times \frac{104}{100} \times \frac{104}{100} \\ A = 5 \times 10816 \\ A = 54080 \\ CI = 54080 - 50000 = 4080 \\ Difference between the interest of on year \\ = 4080 - 4000 \\ = 80 \end{aligned}$

145.

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

146.

Vipul and Manish invested the sum on Rs. 15000 and Rs. 20000 at the rate of 20 percent p.a and 30 percent p.a. respectively on compound interest (compounding annually). If time period is 3 years for both, then what will be the total compound interest earned by Vipul and Manish?

(A) Rs. 29460
(B) Rs. 32480
(C) Rs. 31688
(D) Rs. 34860

Solution: $\begin{aligned} 15000 [{(1 + \frac{20}{100})}^{3} - 1] + 20000 [{(1 + \frac{30}{100})}^{3} - 1] \\ = 15000 (\frac{216}{125} - 1) + 20000 (\frac{2197}{1000} - 1) \\ = 15000 \times \frac{91}{125} + 20000 \times \frac{1197}{1000} \\ = 10920 + 23940 \\ = Rs . 34860 \end{aligned}$

147.

The compound interest on Rs. 30000 at 7% per annum is Rs. 4347. The period (in years) is = ?

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

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

148.

A man borrow Rs. 4000 at 15%, compound rate of interest. At the end of each year he pays back Rs. 1500. How much amount should be pay at the end of the third year to clear all his dues ?

(A) Rs. 874.75
(B) Rs. 824.50
(C) Rs. 924.25
(D) Rs. 974.25

Solution: $\begin{aligned} Amount after 1^{st} year \\ = Rs . [4000 (1 + \frac{15}{100}) - 1500] \\ = Rs . [(4000 \times \frac{23}{20}) - 1500] \\ = Rs . (4600 - 1500) \\ = Rs . 3100 \\ Amount after 2^{nd} year \\ = Rs . [3100 (1 + \frac{15}{100}) - 1500] \\ = Rs . [(3100 \times \frac{23}{20}) - 1500] \\ = Rs . (3565 - 1500) \\ = Rs . 2065 \\ Amount after 3^{rd} year \\ = Rs . [2065 (1 + \frac{15}{100}) - 1500] \\ = Rs . [(2065 \times \frac{23}{20}) - 1500] \\ = Rs . (2374.75 - 1500) \\ = Rs . 874.75 \end{aligned}$

149.

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

150.

On a certain sum of money, the difference between the compound interest for a year payable half yearly, and the simple interest for a year is Rs. 180. If the rate of interest in both the cases is 10%, then the sum is = ?

(A) Rs. 60000
(B) Rs. 72000
(C) Rs. 62000
(D) Rs. 54000

Solution: Rate % = 10%, Time = 1 year Case (I) : When interest is calculated yearly, Rate = 10% Case (II) : When interest is calculated half yearly $\begin{aligned} \Rightarrow New rate % = \frac{10}{2} = 5 % \\ Time = 1 \times 2 = 2 years \\ Effective rate % \\ = 5 + 5 + \frac{5 \times 5}{100} = 10.25 % \\ Difference in rates \\ = (10.25 - 10) % = 0.25 % \\ According to the question, \\ 0 .25% of sum = Rs 180 \\ Sum = \frac{180}{0.25} \times 100 \\ = Rs. 72000 \end{aligned}$

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Practice MCQ Questions and Answer on Compound Interest

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