Practice MCQ Questions and Answer on Interest

11.

What is the amount of equal installment, if a sum of Rs. 1428 due 2 years hence has to be completely repaid in 2 equal annual installments starting next year?.

(A) 700
(B) 800
(C) 650
(D) cannot be determined

Solution: As short - cut of installment for 2 installments is given by Installment = $\frac{P}{(\frac{100}{100} + R) + {(\frac{100}{100} + R)}^{2}}$ There is the need of rate (R) which is unavailable in the question. so, we cannot determine the answer

12.

A sum of Rs. 10 is lent by a child to his friend to be returned in 11 monthly instalment a of Rs. 1 each, the interest being simple. The rate of interest is:

(A) $11 \frac{9}{11} %$
(B) $21 \frac{9}{11} %$
(C) $10 \frac{2}{11} %$
(D) $9 \frac{1}{11} %$

Solution: Let the rate of interest be R% per annum = Amount to be paid. If paid at the end of 11 months $\Rightarrow 10 + \frac{10 \times R \times \frac{11}{12}}{100} = 10 + \frac{11 R}{120}$ Total effective payments = (Rs. 1 + Interest on Rs. 1 for 10 months) + (Rs. 1 + Interest on Rs. 1 for 9 months) + . . . . . + (Rs. 1 + Interest on Rs. 1 for 1 month) + Rs. 1 $\begin{aligned} = (1 + \frac{1 \times R \times \frac{10}{12}}{100}) + (1 + \frac{1 \times R \times \frac{9}{12}}{100}) + . . . . . + (1 + \frac{1 \times R \times \frac{1}{12}}{100}) + 1 \\ = (1 + \frac{10 R}{1200}) + (1 + \frac{9 R}{1200}) + . . . . . + (1 + \frac{R}{1200}) + 1 \\ = 11 + \frac{R (\frac{10 \times 11}{2})}{1200} \\ = 11 + \frac{11 R}{240} \\ Now we have \\ 10 + \frac{11 R}{120} = 11 + \frac{11 R}{240} \\ \frac{11 R}{240} = 1 \\ R = \frac{240}{11} \\ R = 21 \frac{9}{11} % \end{aligned}$

13.

A computer is available for Rs. 39000 cash or Rs. 17000 as cash down payment followed by five monthly instalments of Rs. 4800 each. What is the rate of interest under the instalment plan?

(A) 35.71 % p.a.
(B) 36.71 % p.a.
(C) 37.71 % p.a.
(D) 38.71 % p.a.

Solution: Total cost of the computer = Rs. 39000 Down payment = Rs. 17000 Balance = Rs. (39000 - 17000) = Rs. 22000. Let the rate of interest be R% p.a. Amount of Rs. 22000 for 5 months $\begin{aligned} = Rs . (22000 + 22000 \times \frac{5}{12} \times \frac{R}{100}) \\ = Rs . (22000 + \frac{275 R}{3}) \end{aligned}$ The customer pays the shopkeeper Rs. 4800 after 1 month, Rs. 4800 after 2 months, ...... and Rs. 4800 after 5 months. Thus, the shopkeeper keeps Rs. 4800 for 4 months, Rs. 4800 for 3 months, Rs. 4800 for 2 months, Rs. 4800 for 1 months and Rs. 4800 at the end. ∴ sum of the amounts of these installments = (Rs. 4800 + S.I. on Rs 4800 for 4 months) + (Rs. 4800 + S.I. on Rs. 4800 for 3 months) + ...... + (Rs. 4800 + S.I. on Rs. 4800 for 1 month) + Rs. 4800 = Rs. (4800 × 5) + S.I. on Rs. 4800 for (4 + 3 + 2 + 1) months = Rs. 24000 + S.I. on Rs. 4800 for 10 months $= Rs . (24000 + 4800 \times R \times \frac{10}{12} \times \frac{1}{100}) =$ $Rs . (24000 + 40 R)$ $\begin{aligned} ∴ 22000 + \frac{275 R}{3} = 24000 + 40 R \\ \Rightarrow \frac{155}{3} = 2000 \\ \Rightarrow R = \frac{2000 \times 3}{155} \\ = 38.71 % p .a . \end{aligned}$

14.

Ram deposited a certain sum of money in a company at 12% per annum simple interest for 4 years and deposited equal amounts in fixed deposit in a bank for 5 years at 15% per annum simple interest. If the difference in the interest from two sources is Rs. 1350 then the sum deposited in each case is = ?

(A) Rs. 3000
(B) Rs. 4000
(C) Rs. 6500
(D) Rs. 5000

Solution: Difference between their rates he gained from both boys $\begin{aligned} \Rightarrow (15 \times 5) % - (12 \times 4) % \\ \Rightarrow 75 % - 48 % \\ \Rightarrow 27 % = 1350 (given) \\ \Rightarrow 100 % = Rs . 5000 \end{aligned}$

15.

The simple interest on a sum of money is $\frac{1}{4}$ of the principal and the number of years is equal to rate percent per annum. The rate percent is = ?

(A) 2.5%
(B) 5%
(C) 7.5%
(D) 10%

Solution: $\begin{aligned} Principal Interest \\ \underset{}{\underset{⏟}{4 P P}} \\ Time = Rate % (given) \\ Now by using formula , \\ P = \frac{4 P \times R \times R}{100} \\ \Rightarrow R^{2} = \frac{100}{4} \\ \Rightarrow R = \frac{10}{2} \\ \Rightarrow R = 5 % \end{aligned}$

16.

If the ratio of principal and the simple interest of 5 years is 10 : 3, then the rate of interest is = ?

(A) 6%
(B) 8%
(C) 3%
(D) 5%

Solution: $\begin{aligned} \frac{P}{S .I .} = \frac{10}{3} \\ Let Principal = 10 \\ S .I . for 5 years = 3 \\ S .I . for 1 year = 0 .6 \\ Rate = \frac{S .I .}{Principal} \times 100 \\ Rate = \frac{0.6}{10} \times 100 \\ = 6 % \end{aligned}$

17.

A sum of Rs. 10 is lent to be returned in 11 monthly instalments of Rs. 1 each, interest being simple. The rate of interest is:

(A) $9 \frac{1}{11}$ %
(B) 10%
(C) 11%
(D) $21 \frac{9}{11}$ %

Solution: ⇒ Rs. 10 + S.I. on Rs. 10 for 11 months = Rs. 11 + S.I. on Rs. 1 for (1 + 2 + 3 + 4 + ........... + 10) months ⇒ Rs. 10 + S.I. on Rs. 1 for 110 months = Rs. 11 + S.I. on Rs. 1 for 55 months S.I. on Rs. 1 for 55 months = Rs. 1 $\begin{aligned} ∴ Rate = (\frac{100 \times 12}{1 \times 55}) % \\ = 21 \frac{9}{11} % \end{aligned}$

18.

In how many years will a sum of money double itself at 18.75% per annum simple interest?

(A) 4 years 5 months
(B) 5 years 4 months
(C) 6 years 2 months
(D) 6 year 5 months

Solution: $\begin{aligned} Let sum = Rs . x \\ Then, \\ S .I . = Rs . x \\ ∴ Time = (\frac{100 \times S .I .}{P \times R}) \\ = (\frac{100 \times x}{x \times 18.75}) years \\ = \frac{26}{3} years \\ = 5 \frac{1}{3} years \\ = 5 years 4 months \end{aligned}$

19.

A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?

(A) Rs. 4462.50
(B) Rs. 8032.50
(C) Rs. 8900
(D) Rs. 8925

Solution: $\begin{aligned} Principal \\ = R s . (\frac{100 \times 4016.25}{9 \times 5}) \\ = R s . (\frac{401625}{45}) \\ = R s . 8925 \end{aligned}$

20.

If a certain sum of money becomes doubles at simple interest in 12 years, what would be the rate of interest per annum?

(A) $8 \frac{1}{3}$
(B) 10
(C) 12
(D) 14

Solution: Let, Principal, P = Rs. 100; Amount, A = Rs. 200; Time = 12 years; Interest = Rs. 100; Rate of interest $\begin{aligned} = \frac{Total Interest}{Given Time} \\ = \frac{100}{12} \\ = 8 \frac{1}{3} % \end{aligned}$

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Practice MCQ Questions and Answer on Interest

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