Practice MCQ Questions and Answer on Compound Interest

51.

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

52.

An amount of Rs 6000 lent at 5% per annum compounded interest for 2 years will become = ?

(A) Rs. 600
(B) Rs. 6600
(C) Rs. 6610
(D) Rs. 6615

Solution: $\begin{aligned} Amount = 6000 {(1 + \frac{5}{100})}^{2} \\ \Rightarrow Amount = 6000 \times \frac{21}{20} \times \frac{21}{20} \\ \Rightarrow Amount = Rs. 6615 \end{aligned}$

53.

A certain sum, invested at 4% per annum compound interest, compounded half yearly, amounts to Rs. 7803 at the end of one year. The sum is ?

(A) Rs. 7000
(B) Rs. 7200
(C) Rs. 7500
(D) Rs. 7700

Solution: Time (t) = 1 years Rate % = 4% Amount = Rs. 7803 When interest is compounded half yearly New Rate = $\frac{4}{2}$ = 2% Time = 1 × 2 = 2 years Required rate% for 2 years CI $= 2 + 2 + \frac{2 \times 2}{100} = 4.04 %$ According to question, (100 + 4.04)% of sum = Rs. 7803 $\begin{aligned} ∴ Sum = \frac{7803}{104.04} \times 100 \\ = Rs . 7500 \end{aligned}$

54.

A loan is to be returned in two equal yearly instalments. If the rate of interest is 10% p.a. compounded annually and each instalment is Rs. 5,808, then 60% of the total interest (nearest to a Rs.) charge in this scheme is:

(A) 917
(B) 922
(C) 913
(D) 911

Solution: 10% = $\frac{1}{10}$ $\begin{matrix} Principal Interest \\ I \to & 10_{\times 11 = 110} 11_{\times 11 = 121} \\ II \to & {10^{2}}_{= 100} {11^{2}}_{= 121} \\ Total \to & \overset{―}{\underset{―}{210 242}} \end{matrix}$ Total interest on sum = 242 - 210 = 32 units 121 units → 5808 1 unit → 48 32 units → 48 × 32 = 1536 Total interest of 60% = 1536 × $\frac{60}{100}$ = Rs. 921.6 ∼ Rs. 922

55.

The compound interest on a certain sum of money at a certain rate for 2 years is Rs. 40.80 and the simple interest on the same sum is Rs. 40 at the same rate and for the same time. The rate of interest is = ?

(A) 2% per annum
(B) 3% per annum
(C) 4% per annum
(D) 5% per annum

Solution: Difference in CI and SI for 2 years $\begin{aligned} = (40.80 - 40) \\ = Rs 0 .80 \\ SI for first year \\ = \frac{40}{2} = Rs . 20 \\ Required Rate % \\ = \frac{0.80}{20} \times 100 = 4 % \end{aligned}$

56.

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

57.

There is a 60% increase in an amount in 5 years at simple interest. What will be the compound interest on Rs. 6,250 for two years at the same rate of interest, when the interest is compounded yearly?

(A) Rs. 1,590
(B) Rs. 1,560
(C) Rs. 1,500
(D) Rs. 1,480

Solution: $Rate % = \frac{60}{5} = 12 %$ $159 \to 159 \times 10 = 1590$

58.

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

59.

The simple interest on a sum of money at 4% per annum for 2 years is Rs 80. The compound interest on the same sum for the same period is = ?

(A) Rs. 82.60
(B) Rs. 82.20
(C) Rs. 81.80
(D) Rs. 81.60

Solution: $\begin{aligned} Rate % = 4 % \\ Time (t_{1}) = 2 years \\ SI for 2 years \\ = 4 \times 2 = 8 % \\ CI for 2 years \\ = 4 + 4 + \frac{4 \times 4}{100} \\ = 8.16 % \\ Required C I \\ = \frac{80}{8} \times 8.16 \\ = R s . 81.60 \end{aligned}$

60.

The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:

(A) Rs. 400
(B) Rs. 500
(C) Rs. 600
(D) Rs. 800

Solution: $\begin{aligned} Let the sum be Rs. P \\ Then, P {(1 + \frac{10}{100})}^{2} - P = 525 \\ \Rightarrow P [{(\frac{11}{10})}^{2} - 1] = 525 \\ \Rightarrow P = \frac{525 \times 100}{21} = 2500 \\ ∴ Sum = R s . 2500 \\ So, S.I. = R s . (\frac{2500 \times 5 \times 4}{100}) \\ = R s . 500 \end{aligned}$

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Practice MCQ Questions and Answer on Compound Interest

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