Question

The difference between the compound interest and simple interest for the amount Rs 5000/- in 2 years is Rs. 32. Then the rate of interest per annum is:

• A. 5%
• B. 8%
• C. 10%
• D. 12%

Answer 1

The Correct Option is B

To solve the problem of finding the rate of interest per annum when the difference between compound interest and simple interest for an amount of Rs 5000/- in 2 years is Rs. 32, let's use the formulas for compound interest and simple interest.

Given:

• Principal (P) = Rs 5000 
• Time (T) = 2 years
• Difference between compound interest and simple interest = Rs 32

We need to find the rate of interest per annum (R).

The formula for Simple Interest (SI) is:

\(SI = \frac{P \times R \times T}{100}\)

The formula for Compound Interest (CI) for 2 years is:

\(CI = P \left(1 + \frac{R}{100}\right)^2 - P\)

The difference between CI and SI is given by:

\(CI - SI = \frac{P \times R^2}{100^2}\)

We know this difference is Rs 32, so:

\(\frac{5000 \times R^2}{100^2} = 32\)

Simplifying:

\(\frac{5000 \times R^2}{10000} = 32\)

\(500 \times R^2 = 3200\)

\(R^2 = \frac{3200}{500}\)

\(R^2 = 6.4\)

\(R = \sqrt{6.4} \approx 8\)

Therefore, the rate of interest per annum is 8%.

This matches with the correct option: 8%.