Rs 1500 is invested at 20% per annum, with interest compounded annually, for a period of 3 years. To what amount, in rupees, will this sum grow at the end of the three years?

Introduction / Context:
This question is a direct application of the compound interest concept where interest is compounded annually. The principal amount and the rate of interest per annum are given, and the time period is specified in years. The problem asks for the final amount, which means we need to calculate both the interest and the principal together after three years. Such questions are standard in quantitative aptitude and help assess how well a student can use the compound interest formula and handle percentage growth over multiple periods.

Given Data / Assumptions:

• Principal (P) = Rs 1,500.
• Rate of interest (R) = 20% per annum.
• Time (T) = 3 years.
• Interest is compounded annually, that is, once per year.
• No interim withdrawals or additional deposits are made.

Concept / Approach:
For annual compounding, the standard compound interest amount formula is:
A = P * (1 + R / 100)^THere, A is the amount at the end of T years, P is the original principal, R is the annual rate of interest, and T is the time in years. Once we obtain A, we can recognize that A itself is the required final answer, since the question asks for the amount and not only the interest.

Step-by-Step Solution:
Step 1: Substitute the given values into the formula A = P * (1 + R / 100)^T.Step 2: Here P = 1500, R = 20, and T = 3. So we have A = 1500 * (1 + 20 / 100)^3.Step 3: Compute the term (1 + 20 / 100) = 1 + 0.20 = 1.20.Step 4: Calculate 1.20^3. First 1.20^2 = 1.44, and then 1.44 * 1.20 = 1.728.Step 5: Now multiply the principal by this growth factor: A = 1500 * 1.728.Step 6: Perform the multiplication: 1500 * 1.728 = 2592.Step 7: Therefore, the amount after 3 years is A = Rs.2592.

Verification / Alternative check:
We can also compute year by year to verify. At the end of year 1, amount = 1500 + 20% of 1500 = 1500 + 300 = 1800. End of year 2, amount = 1800 + 20% of 1800 = 1800 + 360 = 2160. End of year 3, amount = 2160 + 20% of 2160 = 2160 + 432 = 2592. This matches the result from the formula, so the calculation is confirmed to be correct.

Why Other Options Are Wrong:
Rs.2352 and Rs.2392 are both less than the correct amount and correspond to an effective growth lower than 20% per year. Rs.2492 is closer but still short of the exact compound interest result, suggesting an incorrect or approximate calculation. Rs.2450 is another distractor that does not come from consistent annual compounding at 20%. Only Rs.2592 matches the correctly computed amount.

Common Pitfalls:
Learners sometimes confuse simple interest and compound interest and may compute 3 years of simple interest as 1500 * 20 * 3 / 100 = 900, giving amount 2400, which is not correct for compounding. Another mistake is to incorrectly square or cube the growth factor, for example, multiplying 1.20 by 3 instead of raising it to the power 3. Careful stepwise work with exponents avoids these errors.

Final Answer:
The amount to which Rs 1,500 will grow in 3 years at 20% per annum, compounded annually, is Rs.2592.