Finding Principal Amount using Interest Difference

We are given the difference between Compound Interest (CI) and Simple Interest (SI) on a principal amount (P) at a rate (R) of 5% per annum for a time period (T) of 2 years is Rs. 15.

Key Information

• Difference (CI - SI) = Rs. 15
• Rate (R) = 5% per annum
• Time (T) = 2 years

Formula for CI and SI Difference (2 Years)

For a time period of 2 years, the difference between CI and SI can be calculated using the formula:

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

Step-by-Step Calculation

1. Substitute the known values into the formula:

   $ 15 = P \left( \frac{5}{100} \right)^2 $

2. Simplify the rate term:

   $ \frac{5}{100} = \frac{1}{20} $

   $ 15 = P \left( \frac{1}{20} \right)^2 $

3. Calculate the square of the rate term:

   $ \left( \frac{1}{20} \right)^2 = \frac{1}{400} $

   $ 15 = P \times \frac{1}{400} $

4. Solve for the Principal (P):

   $ P = 15 \times 400 $

   $ P = 6000 $

Conclusion

The principal amount is Rs. 6,000.