If an increase of 40% is observed on an amount in 4 years at simple interest, what will be the compound interest on
₹80,000 after 4 years at the same rate of interest?

Correct option is D

Given:

Principal (P) = ₹80,000

Time (T) = 4 years

Simple interest increases by 40% in 4 years.

Rate of interest is the same for both simple and compound interest.

Formula Used:

Simple Interest:

SI = $$\frac{P \times R \times T}{100}$$

Compound Interest: CI =$$P \left( 1 + \frac{R}{100} \right)^T - P$$​​

Where:

P = Principal

R= Annual rate of interest

T = Time in years

Solution:

Since the amount increases by 40%, we know that SI = 40% of the principal after 4 years.

SI$$= \frac{40}{100} \times 80,000 = 32,000$$​

Use the formula for SI:

32,0$$00 = \frac{80,000 \times R \times 4}{100}$$​​

32,000 $$= \frac{320,000 R}{100}$$​​

3$$2,000 \times 100 = 320,000 R$$​​

R $$= \frac{32,000 \times 100}{320,000} = 10\%$$​

So, the rate of interest R is 10%.

A =$$80,000 \left( 1 + \frac{10}{100} \right)^4 = 80,000 \left( 1.1 \right)^4$$

A= 80,00$$0 \times 1.4641 =$$​117,128

The compound interest is:

CI = A - P = 117,128 - 80,000 = 37,128

Thus, the compound interest on ₹80,000 after 4 years at the same rate of interest is ₹37,128.

Alternate Method: