Find the compound interest on Rs. 4000 for 4 years at 10% per annum, assuming interest is compounded annually. Give your answer in rupees.

Introduction / Context:
This is a straightforward compound interest computation. We know the principal, the annual interest rate, the duration in years, and that compounding is annual. Our goal is to calculate the total compound interest earned, not just the final amount, over four years at 10% per annum.

Given Data / Assumptions:

Principal P = Rs. 4000
Rate of interest r = 10% per annum
Time t = 4 years
Compounding frequency = annual
We must find CI, the compound interest in rupees

Concept / Approach:
The amount A under compound interest when compounding annually is:
A = P * (1 + r/100)^t. The compound interest is given by:
CI = A − P. We therefore compute the growth factor (1.10)^4, multiply it by the principal to get A, and then subtract the original principal to obtain CI.

Step-by-Step Solution:
Step 1: Compute the growth factor. 1 + r/100 = 1 + 10/100 = 1.10. (1.10)^4 = 1.1 * 1.1 * 1.1 * 1.1 = 1.4641. Step 2: Compute the amount A after 4 years. A = 4000 * 1.4641 = Rs. 5856.40. Step 3: Compute the compound interest CI. CI = A − P = 5856.40 − 4000 = Rs. 1856.40.

Verification / Alternative check:
We can verify by calculating year by year: Year 1 amount = 4000 * 1.1 = 4400. Year 2 amount = 4400 * 1.1 = 4840. Year 3 amount = 4840 * 1.1 = 5324. Year 4 amount = 5324 * 1.1 = 5856.4. Total interest = 5856.4 − 4000 = 1856.4, matching our formula-based result.

Why Other Options Are Wrong:
Rs. 1600 is the simple interest for 4 years at 10% (4000 * 0.10 * 4), not the compound interest. Rs. 1856 is close but slightly underestimates the true value; it looks like a rounded answer that ignores the extra 0.40 rupee. Rs. 1756.60 does not correspond to any correct calculation at 10% with annual compounding. Only Rs. 1856.40 is mathematically correct.

Common Pitfalls:
Some students mistakenly use the simple interest formula or stop after two multiplications instead of four. Others round intermediate values too aggressively, leading to small errors in the final amount. When the question expects a precise decimal answer, carry enough decimal places through the calculation to avoid such discrepancies.

Final Answer:
The compound interest earned over 4 years is Rs. 1856.40.