What is the compound interest on Rs. 5000 for 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 at these varying rates?

Introduction / Context:
Unlike standard compound interest questions with a constant rate, this problem uses different interest rates for each of the three years. This reflects real-life situations where interest rates change over time. The approach is still based on compounding, but we apply each year's rate sequentially to the growing amount.

Given Data / Assumptions:

• Principal P = Rs. 5000
• Rate for year 1 = 4%
• Rate for year 2 = 3%
• Rate for year 3 = 2%
• Compounding takes place annually
• We need the total compound interest over 3 years

Concept / Approach:
When rates vary each year, we multiply the principal by each year's growth factor in sequence. The total amount after 3 years is:
A = P * (1 + 0.04) * (1 + 0.03) * (1 + 0.02)Then compound interest CI is:
CI = A - P

Step-by-Step Solution:
Step 1: Compute the amount after year 1.A1 = 5000 * 1.04 = Rs. 5200Step 2: Compute the amount after year 2 with 3% on A1.A2 = 5200 * 1.03 = Rs. 5356Step 3: Compute the amount after year 3 with 2% on A2.A3 = 5356 * 1.02 = Rs. 5463.12Step 4: Find compound interest.CI = A3 - P = 5463.12 - 5000 = Rs. 463.12

Verification / Alternative check:
We can also calculate using a single combined multiplier: overall factor = 1.04 * 1.03 * 1.02 ≈ 1.092624. Then:
A = 5000 * 1.092624 = 5463.12The difference between amount and principal again gives CI = Rs. 463.12. This matches our stepwise result.

Why Other Options Are Wrong:
Rs. 435.21, Rs. 453.12, Rs. 436.12: These come from misapplying one of the yearly rates or from incorrect multiplication.Rs. 420.00: Too low; it may be an approximation using simple interest ideas instead of compounding.

Common Pitfalls:
Common errors include averaging the rates and using a single rate for all three years, or applying each rate on the original principal instead of the accumulated amount. Always remember that compound interest grows on the updated balance each year, especially when rates change.

Final Answer:
The compound interest on Rs. 5000 for 3 years at rates 4%, 3%, and 2% respectively is Rs. 463.12.