Finding the Principal Sum Using Interest Difference

The question asks us to find the principal sum invested, given the difference between the compound interest (CI) and simple interest (SI) earned over two years at an annual interest rate of 9%. The difference is specified as ₹ 97.2.

Understanding the CI and SI Difference

For a period of two years, the difference between compound interest and simple interest on a principal amount '$P$' at a rate '$R$' percent per annum is calculated using the formula:

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

Applying the Formula and Values

We are given:

• Difference = ₹ 97.2
• Interest Rate ($R$) = 9%

Substitute these values into the formula:

$97.2 = P \times \left(\frac{9}{100}\right)^2$

Calculating the Principal Sum (P)

First, calculate the square of the rate fraction:

$\left(\frac{9}{100}\right)^2 = \frac{81}{10000}$

Now, rewrite the equation:

$97.2 = P \times \frac{81}{10000}$

To find '$P$', rearrange the equation:

$P = 97.2 \times \frac{10000}{81}$

Perform the calculation:

$P = \frac{972}{10} \times \frac{10000}{81}$

$P = \frac{972 \times 1000}{81}$

Since $972 \div 81 = 12$, we get:

$P = 12 \times 1000$

$P = 12000$

Conclusion

The sum invested is ₹ 12,000.