The question asks for the sum of money (Principal, P) given the difference between compound interest (CI) and simple interest (SI) for 2 years at a specific rate.
Calculating the Principal Sum
We are given:
- Rate of Interest (R) = 8% per annum
- Time Period (T) = 2 years
- Difference between CI and SI = ₹240
For a time period of 2 years, the difference between compound interest and simple interest is given by the formula:
Difference = $P \times \left( \frac{R}{100} \right)^2$
Where P is the Principal sum.
Step-by-Step Solution
- Substitute the given values into the formula:
$240 = P \times \left( \frac{8}{100} \right)^2$
- Simplify the term in the parenthesis:
$\frac{8}{100} = \frac{2}{25}$
$240 = P \times \left( \frac{2}{25} \right)^2$
- Calculate the square:
$240 = P \times \frac{4}{625}$
- Rearrange the equation to solve for P:
$P = 240 \times \frac{625}{4}$
- Perform the final calculation:
$P = 60 \times 625$
$P = 37,500$
Therefore, the sum of money is ₹37,500.
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