On an amount, the difference in interests is ₹225 at 10% per annum rate when the interest is compounded semi-annually and annually, respectively, in a year. The amount (in ₹) is:

Correct option is A

Given:

Difference in interest = ₹225

Rate of interest = 10% per annum

Time = 1 year

Compounded semi-annually and annually

Formula Used:

Compound Interest (CI) when compounded annually:

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

where:

A = Amount

P = Principal

r = Rate of interest

t = Time in years

Compound Interest (CI) when compounded semi-annually:

A = $$P \left(1 + \frac{r}{200}\right)^{2t}$$​

Solution:

Let the principal amount be P.

 Amount when compounded annually:

​$$A_{\text{annually}} = P \left(1 + \frac{10}{100}\right)^1 = P \times 1.1$$​

Amount when compounded semi-annually:

​$$A_{\text{semi-annually}} = P \left(1 + \frac{10}{200}\right)^2 = P \times \left(1.05\right)^2 = P \times 1.1025$$​

The difference in interests:

Difference = $$A_{\text{semi-annually}} - A_{\text{annually}} = P \times 1.1025 - P \times 1.1 = P \times (1.1025 - 1.1) = P \times 0.0025$$​

Given that the difference is ₹225:

P × 0.0025 = 225

P =$$\frac{225}{0.0025}$$​ = 90,000

The principal amount is ₹90,000.