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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Important Questions from Simple and Compound Intrest
Amit had invested same amount of sums at simple as well as compound interest, compounded annually. The time period of investment for both the sums was 2 years and rate of interest too was the same, 4% per annum. At the end, he found a difference of ₹43 in both the interests received. What were the sums (in ₹) invested?
When the difference between compound interest, compounded annually, and simple interest for three years is ₹186 at 10% interest per annum, the principal is ₹______.
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