Question

The difference between simple and compound interest on a sum for three years at 5% per annum is Rs. 76.30. Find the sum.

• A. Rs. 9,000
• B. Rs. 10,000
• C. Rs. 11,000
• D. Rs. 11,700

Hint:

Difference between compound and simple interest is small for low rates and short periods; always use the formula \(\text{CI}-\text{SI} = P[(1 + r/100)^n - 1 - n \cdot r/100]\).

Answer 1

The Correct Option is B

Step 1: Recall the formula for the difference between compound interest (CI) and simple interest (SI).
The difference for \(n\) years at rate \(r\) is given by: \( \text{CI} - \text{SI} = P \left(1 + \frac{r}{100}\right)^n - P - P \cdot n \cdot \frac{r}{100} \)
Step 2: Substitute the given values.
\[76.30 = P \left[\left(1 + \frac{5}{100}\right)^3 - 1 - 3 \cdot \frac{5}{100}\right]\] \[76.30 = P \left[(1.05)^3 - 1 - 0.15\right]\] \[(1.05)^3 = 1.157625\] \[1.157625 - 1 - 0.15 = 0.007625\] \[76.30 = P \cdot 0.007625\] \[P = \frac{76.30}{0.007625} = 10,000\]