Govind invested some money in a bank at 4% per annum rate of interest. What would be the corresponding simple interest (in ₹) if after 2 years, Govind got ₹280.5 as compound interest, considering annual compounding?​

Correct option is A

Given:

Compound Interest (CI) after 2 years = ₹280.5

Rate of interest = 4% per annum

Time = 2 years

Interest is compounded annually

We are to find the equivalent Simple Interest (SI) over 2 years at the same rate.

Formulae Used:

Compound Interest (CI):

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

Simple Interest (SI):

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

Solution:

Let the principal be P

Using the CI formula:

280.5 = $$P \left( \left(1 + \frac{4}{100} \right)^2 - 1 \right)$$​​

280.5 =$$P \left( (\frac{676}{625} - 1 \right) = P \left( \frac{51}{625} \right)$$​​

P = $$\frac{280.5\times 625}{51} \approx 3437.5$$​​

Now, 

SI = $$\frac{3437.5 \times 4 \times 2}{100}$$​ = ₹275