What amount will Rs. 1,500 grow to in 3 years if it is invested at 20% per annum compound interest, with interest compounded annually?

Introduction:
This question is a standard compound interest amount problem. We are asked to find the future value of Rs. 1,500 invested for 3 years at a relatively high rate of 20% per annum, compounded annually. It demonstrates how quickly money can grow under compound interest at higher rates.

Given Data / Assumptions:
Principal P = Rs. 1,500. Rate r = 20% per annum. Time t = 3 years. Interest is compounded annually.

Concept / Approach:
The amount under compound interest is given by: A = P * (1 + r/100)^t. Here, (1 + r/100) = 1.20, and we raise this to the power of 3 for 3 years. The amount includes both the original principal and the accumulated interest.

Step-by-Step Solution:
Step 1: Compute the multiplier. 1 + r/100 = 1 + 20/100 = 1.20. Step 2: Raise to the power 3. (1.20)^2 = 1.44. (1.20)^3 = 1.44 * 1.20 = 1.728. Step 3: Compute the amount. A = 1500 * 1.728. 1500 * 1 = 1,500. 1500 * 0.728 = 1092. So A = 1,500 + 1,092 = Rs. 2,592.

Verification / Alternative check:
We can verify year by year. End of year 1: 1500 * 1.2 = 1,800. End of year 2: 1,800 * 1.2 = 2,160. End of year 3: 2,160 * 1.2 = 2,592. This stepwise calculation confirms the same result as the direct formula approach.

Why Other Options Are Wrong:
Rs. 2,492 is slightly low, as if one year of full 20% growth were missed in part. Rs. 2,352 would correspond to a lower effective rate or less than 3 years of compounding. Duplicate Rs. 2,352 and Rs. 2,802 do not match the exact cube of 1.2 multiplied by 1,500.

Common Pitfalls:
Some students may apply simple interest and calculate 1500 + 1500 * 20 * 3 / 100 = 1500 + 900 = 2,400, which underestimates the amount since it ignores interest on interest. Others may miscalculate powers of 1.2. Breaking the calculation into year by year steps is an easy way to avoid mistakes.

Final Answer:
The amount after 3 years at 20% compound interest will be Rs. 2,592.