Compound Interest – Find amount after 2 years at 4% p.a.: If ₹ 7,500 is borrowed at compound interest at the rate of 4% per annum (compounded annually), what amount must be repaid after 2 years?

Introduction / Context:
Compound interest grows money by applying interest on both the original principal and the accumulated interest from previous periods. Here the principal is ₹ 7,500, the annual rate is 4%, and the time is 2 years with annual compounding. We must compute the final amount payable after 2 years.

Given Data / Assumptions:

• Principal P = 7,500
• Rate r = 4% per annum
• Time t = 2 years
• Compounding frequency: annually

Concept / Approach:
For annual compounding, the amount formula is A = P * (1 + r/100)^t. This directly accounts for interest-on-interest each year. We will substitute P = 7,500, r = 4, and t = 2, then evaluate the expression.

Step-by-Step Solution:
Compute yearly factor: (1 + r/100) = 1 + 4/100 = 1.04Raise to the power of the years: (1.04)^2 = 1.0816Multiply by principal: A = 7,500 * 1.0816 = 8,112

Verification / Alternative check:
Break it year by year: After Year 1, amount = 7,500 * 1.04 = 7,800. Interest in Year 2 is 4% of 7,800 = 312. Add to 7,800 → 8,112. This matches the direct formula result.

Why Other Options Are Wrong:
₹ 8,082 and ₹ 8,100 are below the correct compounded value; ₹ 7,800 is just one year of growth; ₹ 8,010 understates the second-year interest-on-interest component.

Common Pitfalls:
Using simple interest (adding 4% twice to the original principal) misses compounding on the first year’s interest. Always apply the exponential factor for compound interest problems.

Final Answer:
₹ 8,112