A certain sum of money invested at Compound Interest, compounded annually, amounts to Rs.338 at the rate of 4% per annum for 2 years. Find the sum.

Correct option is D

Given:

Amount after 2 years = Rs. 338

Rate of interest = 4% per annum

Time = 2 years

Formula Used:

Compound Interest formula for calculating the amount is:

​$$A = P \left( 1 + \frac{r}{100} \right)^t$$​​

Where:

- A = Amount after time t

- P = Principal (Sum)

- r = Rate of interest

- t = Time period

Solution:

We need to find the principal P.

Using the formula:

​$$338 = P \left( 1 + \frac{4}{100} \right)^2\\\ \\338 = P \left( 1.04 \right)^2\\\ \\338 = P \times 1.0816$$​​

Solving for P:

​$$P = \frac{338}{1.0816}$$​​

P = 312.5

Therefore, the sum invested is Rs. 312.5.