Practice MCQ Questions and Answer on Compound Interest

81.

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 = ? $15 % = \frac{3}{20}$ $CI = \frac{129 \times 405}{4} = 13061.25$

82.

A sum of money on compound interest amounts to Rs. 10648 in 3 years and Rs. 9680 in 2 years. The rate of interest per annum is = ?

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

Solution: Let the sum be Rs. P and rate of interest be R% per annum. Then, $\begin{aligned} P {(1 + \frac{R}{100})}^{2} = 9680 . . . . . (1) \\ P {(1 + \frac{R}{100})}^{3} = 10648 . . . . . (2) \end{aligned}$ On dividing equation (2) by (1) : $\begin{aligned} 1 + \frac{R}{100} = \frac{10648}{9680} \\ \Rightarrow \frac{R}{100} = \frac{10648}{9680} - 1 \\ \Rightarrow \frac{R}{100} = \frac{10648 - 9680}{9680} \\ \Rightarrow \frac{R}{100} = \frac{968}{9680} \\ \Rightarrow \frac{R}{100} = \frac{1}{10} \\ \Rightarrow R = \frac{1}{10} \times 100 \\ = 10 % \end{aligned}$

83.

The compound interest on a sum of Rs 5000 at 8% per annum for 9 months when interest is compounded quarterly is = ?

(A) Rs. 300
(B) Rs. 300.12
(C) Rs. 306.04
(D) Rs. 308

Solution: In one year there are 4 quarterly months. ∴ 9 month = 3 quarter New Rate of Interest = $\frac{8}{4}$ = 2% i.e 2% = $\frac{1}{50}$ Total CI = (100 + 100 + 100) + (2 + 2 +2) + 0.04 = Rs.306.04

84.

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. 56. If the rate of interest in both the cases is 16%, then the sum is ?

(A) Rs. 1080
(B) Rs. 7805
(C) Rs. 8750
(D) Rs. 5780

Solution: When the money is compounded half yearly the effective rate of interest for 6 months = $\frac{16}{2}$ = 8% = $\frac{2}{25}$ Let principal = (25)2 = 625 ⇒ 4 units → 56 ⇒ 1 unit → 14 ⇒ Principal = 14 × 625 = Rs. 8750

85.

A sum of money becomes eight times in 3 years, If the rate is compounded annually. In how much time will the same amount at the same compound rate become sixteen times ?

(A) 6 years
(B) 4 years
(C) 8 years
(D) 5 years

Solution: $\begin{aligned} Let principal = P \\ C a s e (I) \\ Time = 3 years, \\ Amount = 8P \\ \Rightarrow 8 P = P {(1 + \frac{R}{100})}^{3} \\ \Rightarrow {(2)}^{3} = {(1 + \frac{R}{100})}^{3} \\ Taking cube root of both sides, \\ \Rightarrow 2 = (1 + \frac{R}{100}) \\ \Rightarrow R = 100 % \\ C a s e (I I) \\ Let after t years it will be 16 times \\ \Rightarrow 16 P = P {(1 + \frac{R}{100})}^{t} \\ \Rightarrow 16 = {(2)}^{t} \\ \Rightarrow {(2)}^{4} = {(2)}^{t} \\ \Rightarrow t = 4 \\ Hence required time \\ (t) = 4 years \end{aligned}$

86.

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

87.

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

88.

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

89.

A certain sum amount to Rs. 15,500 in 2 years at 12% p.a. simple interest. The same sum will amount to what in $1 \frac{1}{2}$ ÃÂÃÂ years at 10% p.a., if the interest is compounded half yearly (nearest to Rs. 1)?

(A) Rs. 14,470
(B) Rs. 15,125
(C) Rs. 14,360
(D) Rs. 13,460

Solution: $\begin{aligned} 15500 - P = \frac{P \times 12 \times 2}{100} \\ 1550000 - 100 P = 24 P \\ 124 P = 1550000 \\ P = \frac{1550000}{124} \\ P = Rs . 12500 \\ Half yearly, Rate = 5 % \end{aligned}$

90.

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

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Practice MCQ Questions and Answer on Compound Interest

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