What will be the total compound interest earned on Rs. 5000 in 3 years, if the rate of interest is 4% for the first year, 3% for the second year, and 2% for the third year, with interest compounded annually?

Introduction / Context:
Compound interest with different rates in different years is a very common aptitude examination pattern. In this problem, the principal is Rs. 5000 and the rate of interest changes every year, so the candidate needs to apply the compound interest idea step by step rather than using a single fixed rate formula. This tests understanding of how the amount grows multiplicatively each year when the rate varies, and how to compute the total compound interest at the end of the full period.

Given Data / Assumptions:

• Principal P = Rs. 5000.
• Time period = 3 years.
• Rate in year 1 = 4% per annum.
• Rate in year 2 = 3% per annum.
• Rate in year 3 = 2% per annum.
• Interest is compounded annually.
• We assume there is no withdrawal or additional deposit during these three years.

Concept / Approach:
For varying yearly rates, we do not use one single formula like P * (1 + r) ^ n with a constant r. Instead, we multiply the principal successively by (1 + r1), then (1 + r2), then (1 + r3). The final amount A after three years is given by A = P * (1 + r1) * (1 + r2) * (1 + r3). The compound interest is then CI = A - P. All rates are converted into fractional form before calculation, such as 4% = 0.04 and so on.

Step-by-Step Solution:
Step 1: Convert rates into decimal form: r1 = 4% = 0.04, r2 = 3% = 0.03, r3 = 2% = 0.02. Step 2: Write the amount formula for varying rates: A = 5000 * (1 + 0.04) * (1 + 0.03) * (1 + 0.02). Step 3: Compute the first factor: 1 + 0.04 = 1.04. Step 4: Compute the second factor: 1 + 0.03 = 1.03. Step 5: Compute the third factor: 1 + 0.02 = 1.02. Step 6: Multiply the three factors: 1.04 * 1.03 * 1.02 = 1.092624 (using normal multiplication). Step 7: Multiply by the principal: A = 5000 * 1.092624 = 5463.12. Step 8: Compute the compound interest: CI = A - P = 5463.12 - 5000 = 463.12. Step 9: Thus the required compound interest is Rs. 463.12.

Verification / Alternative check:
A quick reasonableness check is useful. The average of the three annual rates is roughly between 3% and 4%. If we roughly assumed 3% per year on Rs. 5000, the simple interest for three years would be about 5000 * 0.03 * 3 = Rs. 450. Because compound interest will be slightly higher than simple interest at similar rates, a value slightly more than Rs. 450 is expected. The computed figure Rs. 463.12 lies just above this rough estimate, so the answer is very reasonable and consistent with expectations.

Why Other Options Are Wrong:
Rs. 435.21 is too low and does not match the correct product of the three yearly multipliers; it suggests that at least one rate was applied incorrectly or treated as simple interest. Rs. 453.12 is close but still below the correct value and likely results from rounding or from applying only two years of compounding correctly. Rs. 436.12 is again off and does not fit the multiplicative pattern. Rs. 473.12 is slightly higher than the correct interest and comes from overestimating at least one year or using a higher effective rate than the actual combination of 4%, 3%, and 2%.

Common Pitfalls:
A common mistake is to average the three percentages and treat the situation as a simple interest problem with that average rate. Another frequent error is to apply all three rates additively inside a single parenthesis as 1 + (0.04 + 0.03 + 0.02) instead of multiplying three separate factors. Some learners also forget that the interest of one year increases the principal for the next year in compound interest, which is the key to this topic. Careless calculator usage and rounding each intermediate step too early can also move the final answer away from the precise value of Rs. 463.12.

Final Answer:
The compound interest earned on Rs. 5000 over the three years with yearly rates of 4%, 3%, and 2% compounded annually is Rs. 463.12, which corresponds to option D.