Mr Mike borrows Rs 8500 at 4% per annum compound interest, compounded annually. What is the compound interest for 2 years on this loan?

Introduction / Context:
This problem asks specifically for the compound interest, not the total amount, on a loan of Rs 8500 at 4% per annum for 2 years with annual compounding. It tests the ability to distinguish between the amount and the interest part and to apply the compound interest formula correctly.

Given Data / Assumptions:

• Principal P = Rs 8500.
• Rate of interest r = 4% per annum.
• Time t = 2 years.
• Interest is compounded annually.
• We must find the compound interest only.

Concept / Approach:
The compound amount A after t years is:
A = P * (1 + r / 100)^t The compound interest CI is the excess of the amount over the principal:
CI = A - P So we compute A using the formula, then subtract P to obtain CI.

Step-by-Step Solution:
P = 8500, r = 4%, t = 2 years. Amount factor = (1 + 4 / 100)^2 = (1.04)^2. (1.04)^2 = 1.0816. Amount A = 8500 * 1.0816 = Rs 9193.6. Compound interest CI = A - P = 9193.6 - 8500 = Rs 693.6.

Verification / Alternative Check:
We can compute year by year. End of year 1: amount = 8500 + 8500 * 4 / 100 = 8500 + 340 = 8840. End of year 2: interest on 8840 = 8840 * 4 / 100 = 353.6. Final amount = 8840 + 353.6 = 9193.6. CI = 9193.6 - 8500 = Rs 693.6, which matches the earlier calculation.

Why Other Options Are Wrong:
Rs. 9139.6 and Rs. 9193.6 are both total amounts, not compound interest, and only Rs. 9193.6 is the correct amount. Rs. 639.6 is too low and corresponds to an incorrect interest calculation. Only Rs. 693.6 represents the correct compound interest for 2 years at 4%.

Common Pitfalls:
Confusing the total amount with the interest is a very common mistake. Another error is to compute simple interest for 2 years and treat it as compound interest, which gives a slightly smaller value.

Final Answer:
The compound interest on Rs 8500 at 4% per annum for 2 years is Rs. 693.6.