Question

A loan of 1,02,000 is to be paid back in two equal annual instalments. If the rate of interest is 4% p.a., compounded annually, then the total interest charged (in ₹) under this instalment plan is:

• A. 6,000
• B. 6,080
• C. 6,160
• D. 6,200

Hint:

In compound interest problems, always account for the interest that accumulates on both the principal and the interest from previous years.

Answer 1

The Correct Option is C

Let the total loan amount be ₹1,02,000. The loan is to be paid in two equal instalments. The amount for each instalment will be: \[ \frac{1,02,000}{2} = 51,000 \] Since the interest is compounded annually at 4%, the amount to be repaid in the first year will be ₹51,000 + interest on ₹51,000. Using the compound interest formula, the interest for the first year will be: \[ \text{Interest} = 51,000 \times \frac{4}{100} = 2,040 \] The second instalment will have interest on ₹51,000 + ₹2,040 (from the first year), i.e., ₹53,040. Thus, the interest for the second year is: \[ \text{Interest} = 53,040 \times \frac{4}{100} = 2,121.60 \] The total interest charged will be: \[ 2,040 + 2,121.60 = 6,160 \] Thus, the correct answer is 6,160.