Compound Interest - Aptitude MCQ Questions and Solutions with Explanations

41

In how many years will a sum of Rs. 320 amount to Rs. 405 if interest is compounded at 12.5% per annum?

A) 2 years B) 1 year C) $$2\frac{1}{2}{\text{ years}}$$ D) $$1\frac{1}{2}{\text{ years}}$$

Discuss

Answer & Solution

Answer: Option A

Solution:

\[\begin{array}{*{20}{c}} {320}&:&{405} \\ {\sqrt {64} }&:&{\sqrt {81} } \\ 8&:&9 \end{array}\]
$$\eqalign{ & 12\frac{1}{2}\% \to \frac{1}{8} \cr & {\text{In one year}} = 8:9 \cr & {\text{Time}} = 2{\text{ years}} \cr} $$

42

A sum of Rs. 4,620 is to be paid back in 2 equal annual instalments. How much is each instalments (in Rs.) if the interest is compounded annually at 10% per annum?

A) 2,420 B) 2,552 C) 2,662 D) 2,750

Discuss

Answer & Solution

Answer: Option C

Solution:

$$\eqalign{ & P = {\text{Rs}}{\text{. }}4620 \cr & R = 10\% = \frac{1}{{10}} \cr} $$
\[\begin{array}{*{20}{c}} {{\text{Principal}}}&{{\text{Instalments}}} \\ {110 = 10 \times 11}&{11 \times 11 = 121} \\ {100 = 100}&{121} \\ \begin{gathered} 210 \hfill \\ \,\,\,\,\,{ \downarrow ^{ \times 22}} \hfill \\ \end{gathered} &\begin{gathered} \hfill \\ \,\,\,\,\,{ \downarrow ^{ \times 22}} \hfill \\ \end{gathered} \\ {4620}&{{\text{Rs}}{\text{. }}{\mathbf{2662}}} \end{array}\]

43

A sum of Rs. 18,000 is lent at 10% p.a. compound interest, compounded annually. What is the difference between the compound interest for 3^rd year and 4^th year?

A) Rs. 215.40 B) Rs. 217.80 C) Rs. 220.60 D) Rs. 221.80

Discuss

Answer & Solution

Answer: Option B

Solution:

Difference of compound interest = 131 - 10 = 121
10000 → 18000
1 → 1.8
121 → 121 × 1.8 = 217.8

44

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 if Rs. 5,808, then the total interest charged in this scheme is:

A) Rs. 1,563 B) Rs. 1,536 C) Rs. 1,632 D) Rs. 1,602

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & 5808 \times \frac{{10}}{{11}} \times \frac{{21}}{{11}} \cr & {\text{Principal}} = 10080 \cr & {\text{Amount}} = 5808 \times 2 = 11616 \cr & {\text{Interest}} = 1536 \cr} $$

45

What is the amount (in Rs.) of a sum of Rs. 32,000 at 20% per annum for 9 months, compounded quarterly?

A) 37,044 B) 35,087 C) 32,000 D) 30,876

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{Principal}} = {\text{Rs}}{\text{. }}32000 \cr & {\text{Rate}} = 20\% {\text{ p}}{\text{.a}}{\text{.}} \cr & = \frac{{20}}{4}\% = 5\% {\text{ quarterly}} = \frac{1}{{20}} \cr & {\text{Time}} = 9{\text{ months}} = \frac{9}{{12}} \times 4 = 3 \cr} $$
\[\begin{array}{*{20}{c}} {{\text{Principal}}}&{}&{{\text{Amount}}} \\ {{{\left( {20} \right)}^3}}&:&{{{\left( {21} \right)}^3}} \\ {8000}&:&{9261} \\ {\,\,\,\,\,{ \downarrow ^{ \times 4}}}&{}&{\,\,\,\,\,{ \downarrow ^{ \times 4}}} \\ {{\text{Rs}}{\text{. }}32000}&{}&{\boxed{{\text{Rs}}{\text{. }}37044}} \end{array}\]

46

The compound interest on a sum of Rs. 5,500 at 15% p.a. for 2 years, when the interest is compounded 8 monthly is:

A) Rs. 1,850 B) Rs. 1,880 C) Rs. 1,820.50 D) Rs. 1,773.75

Discuss

Answer & Solution

Answer: Option C

Solution:

12 months ⟶ 15%
8 months ⟶ 10%
Compound Interest mcq question image

1000 units ⟶ 5500
1 unit ⟶ 5.5
331 units ⟶ 331 × 5.5 = Rs. 1820.50

47

The compound interest (compounded annually) on a sum of money invested for three years yields Rs. 800 and Rs. 840 in four years. The annual percentage rate of interest is:

A) 4.5% B) 5.5% C) 5% D) 6%

Discuss

Answer & Solution

Answer: Option C

Solution:

Interest of 1 year = 840 - 800 = 40
Rate = $$\frac{{40}}{{50}}$$ × 100 = 5% Answer

48

The compound interest on a sum of Rs. 20,000 at 15% p.a., for $$2\frac{2}{3}$$ years, interest compounded yearly is:

A) Rs. 9,098 B) Rs. 8.896 C) Rs. 9,000 D) Rs. 9,095

Discuss

Answer & Solution

Answer: Option D

Solution:

49

The difference between the compound interest on a sum of Rs. 8,000 for 1 year at the rate of 10% per annum, interest compounded yearly and half yearly is:

A) Rs. 20 B) Rs. 40 C) Rs. 30 D) Rs. 10

Discuss

Answer & Solution

Answer: Option A

Solution:

Principal = Rs. 8000
Rate = 10% p.a. = 5% half per yearly
Time = 1 year
Compound interest yearly = $$\frac{1}{{10}}$$ = Rs. 800
10 unit ⟶ Rs. 8000
1 unit ⟶ Rs. 800
Compound interest half yearly = $$\frac{1}{{20}}$$
400 unit ⟶ 8000
1 unit ⟶ 20
41 unit ⟶ 20 × 41 = Rs. 820
Compound Interest mcq question image

Difference = 820 - 800 = Rs. 20

50

If the difference between the compound interest and simple at 17% on a sum money for 2 years (compounded annually) is Rs. 433.50, then the compounded interest (in Rs.) is:

A) 2,500 B) 2,735.50 C) 5,533.50 D) 5,100

Discuss

Answer & Solution

Answer: Option C

Solution:

$$\eqalign{ & {\text{CI}} - {\text{SI}} = \frac{{17 \times 17}}{{100}} = 2.89\% \cr & 2.89\% \to 433.50 \cr & 1\% \to 150 \cr & 100\% \to 15000 \cr & {\text{CI}} = 17 + 17 + 2.89 = 36.89\% \cr & 36.89\% \to 150 \times 36.89 = 5533.50 \cr} $$