Practice MCQ Questions and Answer on Compound Interest

A sum of money after a period of 2 years becomes Rs. 34,560, and it becomes Rs. 41,472 after a period of three years, being compounded at 'R' rate of interest. What is the value of R?

(A) 20%
(B) 12%
(C) 25%
(D) 10%

Solution: $\begin{aligned} CI of 1 year = 41472 - 34560 = 6912 \\ Rate % = \frac{6912}{34560} \times 100 \\ = 2 \times 10 \\ = 20 % Answer \end{aligned}$

A sum of money invested at compound interest amounts to Rs. 650 at the end of first year and Rs. 676 at the end of second year. The sum of money is = ?

(A) Rs. 600
(B) Rs. 540
(C) Rs. 625
(D) Rs. 560

Solution: Interest on 650 for one year = 676 - 650 = 26 $\begin{aligned} 26 = \frac{650 \times r \times 1}{100} \\ r = 4 % \\ 650 = P [1 + \frac{4}{100}] \\ \Rightarrow 650 = P \times \frac{26}{25} \\ \Rightarrow p = \frac{650 \times 25}{26} \\ = Rs . 625 \end{aligned}$

At a certain rate per annum, the simple interest on a sum of money for one year is Rs. 260 and the compound interest on the same sum for two years is Rs. 540.80. The rate of interest per annum is = ?

(A) 4%
(B) 6%
(C) 8%
(D) 10%

Solution: $\begin{aligned} SI for 1 year \\ = Rs 260 \\ SI for 2 year \\ = 260 \times 2 \\ = Rs . 520 \\ Difference in (CI - SI) \\ (540.80 - 520) = Rs 20 .8 \\ Required rate % \\ = \frac{20.8}{260} \times 100 \\ = 8% \end{aligned}$

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: Amount of Rs. 100 for 1 year when compounded half yearly $\begin{aligned} = Rs . [100 \times {(1 + \frac{3}{100})}^{2}] \\ = Rs .106 .09 \\ ∴ Effective rate \\ = (106.09 - 100) % \\ = 6.09 % \end{aligned}$

The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:

(A) 3
(B) 4
(C) 5
(D) 6

Solution: $\begin{aligned} P {(1 + \frac{20}{100})}^{n} > 2 P \Rightarrow {(\frac{6}{5})}^{n} > 2 \\ Now, (\frac{6}{5} \times \frac{6}{5} \times \frac{6}{5} \times \frac{6}{5}) > 2 \\ S o, n = 4 years \end{aligned}$

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. 520
(B) Rs. 550
(C) Rs. 500
(D) Rs. 515

Solution: $\begin{aligned} 10 % = \frac{1}{10} \\ Let P = {(10)}^{2} = 100 \\ Total CI = 21 unit = 525 \\ 1 unit = 25 \\ P = 100 unit \\ = 100 \times 25 = 2500 \\ New Time = 4 years \\ and new rate = 5 % \\ SI = \frac{2500 \times 4 \times 5}{100} \\ SI = Rs. 500 \end{aligned}$

The principal which will amounts to Rs. 270.40 in 2 years at the rate of 4% per annum compound interest, is = ?

(A) Rs. 200
(B) Rs. 225
(C) Rs. 250
(D) Rs. 220

Solution: $\begin{aligned} 4 % = \frac{1}{25} \\ = \frac{26 \to Amount}{25 \to Principal} \\ Time = 2 years \\ Principal Amount \\ 25 26 \\ 25 26 \\ _______________ \\ 625 676 \\ ↓ \times 0.4 ↓ \times 0.4 \\ 250 270.40 \\ Hence required principal \\ = Rs.250 \end{aligned}$

A sum of Rs. 13360 was borrowed at $8 \frac{3}{4}$ % per annum compound interest and paid back in two years in two equal annual installments. What was the amount of each installment ?

(A) Rs. 5769
(B) Rs. 7569
(C) Rs. 7009
(D) Rs. 7500

Solution: $\begin{aligned} Rate of interest (r) \\ = 8 \frac{3}{4} % = \frac{7}{80} = \frac{87 \to Installment}{80 \to Principal} \end{aligned}$ ⇒ I 80×87 → 87×87 ......(i) ⇒ II 6400 → 7569 ......(ii) Since, installment is equal hence multiply equation (i) by 87 ⇒ Total principal = 6960 + 6400 = 13360 ⇒ 13360 units = Rs. 13360 ⇒ 1 units = Rs. 1 ⇒ 7569 units = Rs. 7569 ∴ Each installment = Rs. 7569

A certain loan was returned in two equal half yearly installments each of Rs. 6760. If the rate of interest was 8% p.a. compounded yearly, how much was the interest paid on the loan?

(A) Rs. 790
(B) Rs. 770
(C) Rs. 750
(D) Rs. 810

Solution: 8% → yearly 4% → half yearly 4 → $\frac{1}{25}$

10.

The compound interest on Rs. 4,000 after 3 year is Rs. 630.50. Then the rate of interest compounded yearly is:

(A) 7%
(B) 5%
(C) 8%
(D) 6%

Solution: $\begin{aligned} 4630.50 = 4000 {(1 + \frac{R}{100})}^{3} \\ 9261 = 8000 {(1 + \frac{R}{100})}^{3} \\ \frac{9261}{8000} = {(1 + \frac{R}{100})}^{3} \\ {(\frac{21}{20})}^{3} = {(1 + \frac{R}{100})}^{3} \\ \frac{21}{20} = (1 + \frac{R}{100}) \\ \frac{1}{20} = \frac{R}{100} \\ R = 5 \end{aligned}$

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Practice MCQ Questions and Answer on Compound Interest

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