Practice MCQ Questions and Answer on Compound Interest

151.

Find the rate percent per annum if Rs. 2000 amounts to Rs. 2315.25 in one and half years interest being compounded half yearly.

(A) 10%
(B) 11.5%
(C) 5%
(D) 20%

Solution: $\begin{aligned} According to the question, \\ compounded half yearly \\ Rate = \frac{R}{2} \\ Time = \frac{2T}{3} \\ Amount = P {(1 + \frac{R}{2 \times 100})}^{3} \\ \Rightarrow 2315.25 = 2000 {(1 + \frac{R}{2 \times 100})}^{3} \\ \Rightarrow \frac{2315.25}{2000} = {(1 + \frac{R}{2 \times 100})}^{3} \\ \Rightarrow \frac{231525}{200000} = {(1 + \frac{R}{2 \times 100})}^{3} \\ \Rightarrow \frac{9261}{8000} = {(1 + \frac{R}{2 \times 100})}^{3} \\ \Rightarrow {(\frac{21}{20})}^{3} = {(1 + \frac{R}{2 \times 100})}^{3} \\ \Rightarrow 1 + \frac{R}{200} = \frac{21}{20} \\ \Rightarrow R = 10 % \end{aligned}$

152.

At what rate percent per annum of compound interest, will a sum of money become four times of itself in two years ?

(A) 100%
(B) 75%
(C) 50%
(D) 20%

Solution: $\begin{aligned} Principal Amount \\ 1 \to 4 \\ \Rightarrow 4 = 1 {(1 + \frac{r}{100})}^{2} \\ \Rightarrow 4 = {(1 + \frac{r}{100})}^{2} \\ \Rightarrow r = 100 % \\ Alternate \\ Principal Amount \\ \sqrt[2]{1} \to \sqrt[2]{4} \\ 1 \to 2 \\ \Rightarrow Rate of interest \\ = \frac{(2 - 1)}{1} \times 100 = 100 % \end{aligned}$

153.

One can purchase a flat from a house building society for Rs. 55000 cash or on the terms that he should pay Rs. 4275 as cash down payment and get the rest in three equal installments. The society charges interest at the rate of 16% per annum compounded half-yearly. If the flat is purchased under installment plan, find the value of each installment ?

(A) Rs. 18756
(B) Rs. 19292
(C) Rs. 19683
(D) Rs. 20285

Solution: Total cost of the flat = Rs. 55000 Down payment = Rs. 4275 Balance = Rs. (55000 - 4275) = Rs. 50725 Rate of interest = 8% per half year Let the value of each instalment be Rs. x P.W. of Rs. x due 6 months hence + P.W. of Rs. x due 1 year hence + P.W. of Rs. x due $1 \frac{1}{2}$ years hence = 50725 $\Rightarrow \frac{x}{(1 + \frac{8}{100})} +$ $\frac{x}{{(1 + \frac{8}{100})}^{2}} +$ $\frac{x}{{(1 + \frac{8}{100})}^{3}} =$ $50725$ $\begin{aligned} \Rightarrow \frac{25 x}{27} + \frac{625 x}{729} + \frac{15625 x}{19683} = 50725 \\ \Rightarrow \frac{50725 x}{19683} = 50725 \\ \Rightarrow x = (\frac{50725 \times 19683}{50725}) = 19683 \end{aligned}$

154.

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

155.

What is the difference between the compound interests on Rs. 5000 for $1 \frac{1}{2}$ years at 4% per annum compounded yearly and half-yearly?

(A) Rs. 2.04
(B) Rs. 3.06
(C) Rs. 4.80
(D) Rs. 8.30

Solution: $\begin{aligned} C .I . when interest compounded yearly \\ = R s . [5000 \times (1 + \frac{4}{100}) \times (1 + \frac{\frac{1}{2} \times 4}{100})] \\ = R s . (5000 \times \frac{26}{25} \times \frac{51}{50}) \\ = R s .5304 \\ C .I . when interest in compounded half - yearly \\ = R s . [5000 \times {(1 + \frac{2}{100})}^{3}] \\ = R s . (5000 \times \frac{51}{50} \times \frac{51}{50} \times \frac{51}{50}) \\ = R s . 5306.04 \\ ∴ Difference = R s . (5306.04 - 5304) \\ = R s . 2.04 \end{aligned}$

156.

The compound interest on Rs. 30000 at 7% per annum for a certain time is Rs. 4347. The times is = ?

(A) 3 years
(B) 4 years
(C) 2 years
(D) 2.5 years

Solution: $\begin{aligned} Principal = Rs . 30000 \\ CI = Rs 4347 \\ Rate = 7 % \\ By using formula, \\ \Rightarrow (30000 + 4347) = 30000 {(1 + \frac{7}{100})}^{t} \\ \Rightarrow 34347 = 30000 {(1 + \frac{7}{100})}^{t} \\ \Rightarrow \frac{34347}{30000} = {(\frac{107}{100})}^{t} \\ \Rightarrow (\frac{11449}{10000}) = {(\frac{107}{100})}^{t} \\ \Rightarrow {(\frac{107}{100})}^{2} = {(\frac{107}{100})}^{t} \\ \Rightarrow t = 2 years \end{aligned}$

157.

A sum of Rs. 10,500 amounts to Rs. 13,650 in 2 years a certain rate percent annum simple interest. The same sum will amount to what in 1 year at the same rate, if the interest in compounded half yearly (nearest to Rs. 1)

(A) Rs. 12,124
(B) Rs. 12,134
(C) Rs. 12,143
(D) Rs. 12,314

Solution: $P = 10500 \overset{2 year}{\to} 13650$ $\begin{aligned} 2 year \to 3150 \\ 3150 = \frac{10500 \times R \times 2}{100} \\ R = 15 % \\ A = 10500 {(1 + \frac{15}{200})}^{2} \\ = 10500 \times \frac{215 \times 215}{200 \times 200} \\ = \frac{105 \times 43 \times 43}{16} \\ = 12134 \end{aligned}$

158.

The simple interest on a sum of money at 10% per annum for 2 years is Rs. 8,100. What would be the compound interest (in Rs.) on the same sum for the same period at 15% p.a, when the interest is compound yearly?

(A) 13061.25
(B) 14671
(C) 8100
(D) 12751

Solution: R = 10%, T = 2 year, SI = Rs. 8100 $8100 = \frac{P \times 10 \times 2}{100}$ 40500 = P Now same principal R% = 15% T = 2 year CI = ? $15 % = \frac{3}{20}$ $CI = \frac{129 \times 405}{4} = 13061.25$

159.

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

160.

What will be the simple to compound interest (compounded annually) ratio on two identical funds put in a bank at an interest rate of 8% (per annum) for three years?

(A) 3 : 5
(B) 1875 : 2029
(C) 3 : 4
(D) 243 : 342

Solution: $8 % = \frac{2}{25}$ $Simple Interest = \frac{15625 \times 8 \times 3}{100} = 3750$ $\begin{matrix} \Rightarrow & Simple Interest & : & Compound Interest \\ 3750 & : & 4058 \\ 1875 & : & 2029 \end{matrix}$

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Practice MCQ Questions and Answer on Compound Interest

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