Question

The difference between the compound interest, compounded annually and the simple interest on a certain sum for 2 years at 6% per annum is Rs.18. Find the sum.

• A. Rs. 4,500
• B. Rs. 5,500
• C. Rs. 5,300
• D. Rs. 5,000

Hint:

The difference in compound and simple interest over short periods like 2 years can be used to calculate principal by setting up an equation from their respective formulas.

Answer 1

The Correct Option is D

Step 1: Establish the formulas for compound interest (CI) and simple interest (SI). \[ \text{Simple Interest (SI)} = P \times r \times t \] \[ \text{Compound Interest (CI)} = P \left(1 + \frac{r}{100}\right)^t - P \] Where \( P \) is the principal, \( r = 6% \), and \( t = 2 \) years.

Step 2: Calculate the difference between CI and SI. \[ \text{Difference} = \text{CI} - \text{SI} = 18 \] \[ P \left(1 + \frac{6}{100}\right)^2 - P - (P \times 0.06 \times 2) = 18 \] \[ P \left(1.1236 - 1 - 0.12\right) = 18 \] \[ P \times 0.0036 = 18 \] \[ P = \frac{18}{0.0036} = 5000 \]