The compound interest on a certain amount for 2 years at 4% per annum is ₹ 1,020, if interest is compounded annually. Find the simple interest on that amount for 2 years at 4% per annum ?

Correct option is D

Given:

Compound Interest (CI) for 2 years = ₹ 1,020

Rate of Interest (R) = 4% per annum

Time (T) = 2 years

Formula Used:

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

Simple Interest (SI) formula:
SI =$$\frac{P \times R \times T}{100}$$​​

Solution:

First, we will calculate the principal amount (P) using the compound interest formula. We know that CI = ₹ 1,020, R = 4%, and T = 2 years.

​$$1020 = P \times \left( \left( 1 + \frac{4}{100} \right)^2 - 1 \right) \\ \ \\1020 = P \times \left( \left( 1 + 0.04 \right)^2 - 1 \right)\\ \ \\1020 = P \times \left( 1.0816 - 1 \right)\\ \ \\1020 = P \times 0.0816\\ \ \\P = \frac{1020}{0.0816} = ₹ 12,500$$​​

Now, we will calculate the simple interest (SI) for the same principal (₹ 12,500) for 2 years at 4% per annum using the formula for SI:

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

SI$$= \frac{12,500 \times 4 \times 2}{100}$$​

SI = $$\frac{100,000}{100}$$​= ₹ 1,000

The simple interest on the amount for 2 years at 4% per annum is ₹ 1,000.