On a certain sum of money, the Simple Interest for 2 years is Rs.140 at 4% per annum. Find the difference between Compound Interest and Simple Interest on the same sum at same rate and same period.

Correct option is B

Given:

Simple Interest (SI) for 2 years = Rs.140

Rate of interest = 4% per annum

Time period = 2 years

.Formula Used:

Simple Interest (SI) = (Principal × Rate × Time) / 100

Solution:

Calculate the principal amount:

SI = (P × 4 × 2) / 100 = Rs.140

P × 8 / 100 = 140

P = 140 × 100 / 8 = Rs.1750

Calculate the Compound Interest for 2 years:

​$$\text{CI} = P \times \left[ \left(1 + \frac{r}{100}\right)^n - 1 \right] \\\ \\\text{CI} = 1750 \times \left[ \left(1 + \frac{4}{100}\right)^2 - 1 \right] \\\ \\\text{CI} = 1750 \times \left[ (1.04)^2 - 1 \right] \\\ \\\text{CI} = 1750 \times \left[ 1.0816 - 1 \right] = 1750 \times 0.0816 = \text{Rs.} 142.8$$

Difference = CI - SI = 142.8 - 140 = Rs.2.8

The difference between Compound Interest and Simple Interest on the same sum at the same rate and for the same period is Rs.2.8.

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