The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 16% per annum is ₹797. Find the sum (rounded off to the nearest integer).​

Correct option is D

Given:

The difference between the simple interest (SI) and compound interest (CI) for 2 years = ₹797

Rate of interest (R) = 16% per annum

Time (T) = 2 years

Formula Used:

The formula for the difference between simple interest and compound interest for 2 years is:

$$\text{CI} - \text{SI} = P \times \left( \frac{R}{100} \right)^2$$​​

where:

P is the principal sum,

R is the annual rate of interest.

Solution:

Substitute the given values into the formula:

797 = $$P \times \left( \frac{16}{100} \right)^2$$​​

P = $$\frac{797 \times 100 \times 100}{16 \times 16}$$​ = 31132.8

Round to the nearest integer:

P = ₹31133