Calculate Interest Rate: CI vs SI Difference

The problem asks for the annual rate of interest given the principal amount, the time period, and the difference between compound interest (compounded annually) and simple interest.

Given:

• Principal (P) = Rs. 80,000
• Time (T) = 2 years
• Difference between CI and SI = Rs. 288

Formula for CI and SI Difference

For a time period of 2 years, the difference between compound interest (CI) and simple interest (SI) is given by the formula:

$ \text{Difference} = P \times \left(\frac{R}{100}\right)^2 $

Where:

• P = Principal amount
• R = Rate of interest per annum (%)

Applying the Formula

Substitute the given values into the formula:

$ 288 = 80000 \times \left(\frac{R}{100}\right)^2 $

Solving for the Rate (R)

1. Isolate the term containing R:

   $ \left(\frac{R}{100}\right)^2 = \frac{288}{80000} $

2. Simplify the fraction:

   $ \left(\frac{R}{100}\right)^2 = \frac{144}{40000} $

   $ \left(\frac{R}{100}\right)^2 = \frac{36}{10000} $

3. Take the square root of both sides:

   $ \frac{R}{100} = \sqrt{\frac{36}{10000}} $

   $ \frac{R}{100} = \frac{6}{100} $

4. Solve for R:

   $ R = 6 $

Therefore, the rate of interest is 6% per annum.