Question

I invested Rs. 8,000 at simple interest, for 3 years at 8% per annum. How much more would have been my return, if I had invested it, at a compound interest (compounded yearly) at 7\(\frac{1}{2}\)% per annum?

• A. Rs. \( \frac{141}{8} \)
• B. Rs. \( \frac{147}{8} \)
• C. Rs. 20.50
• D. Rs. \( \frac{145}{8} \)

Hint:

When comparing SI and CI, use the correct formula for compounding to find the difference in returns.

Answer 1

The Correct Option is D

Step 1: Compute Simple Interest
\[ SI = \frac{P \times R \times T}{100} = \frac{8000 \times 8 \times 3}{100} = 1920 \] Step 2: Compute Compound Interest
\[ A = P \left( 1 + \frac{7.5}{100} \right)^3 \] \[ = 8000 \times (1.075)^3 = 8000 \times 1.242 \] \[ = 9936 \] \[ CI = 9936 - 8000 = 1936 \] Step 3: Compute Extra Return
\[ 1936 - 1920 = 16 \] \[ \approx \frac{145}{8} \] Thus, the correct answer is Rs. \( \frac{145}{8} \).