Sunil invests a certain principal at a compound interest rate of 8% per annum. At the end of 2 years, the compound interest earned on this amount is Rs 2828.80. What is the total amount (principal plus compound interest) that Sunil receives at the end of 2 years?

Introduction / Context:
This question checks the concept of compound interest over a period of 2 years and asks for the final amount, that is, the sum of principal and interest. Instead of directly giving the principal, the problem provides the compound interest earned, and we have to work backwards to find the principal and then the total amount that Sunil receives after 2 years.

Given Data / Assumptions:

• Rate of compound interest = 8% per annum.
• Time period = 2 years.
• Compound interest for 2 years = Rs 2828.80.
• Interest is compounded annually.

Concept / Approach:
For annual compounding, the amount A after 2 years on principal P at rate r percent per annum is given by:
A = P * (1 + r / 100)^2 The compound interest CI is:
CI = A - P We are given CI and r and need to find P using the relation between CI and P for 2 years, and then compute A = P + CI.

Step-by-Step Solution:
Let P be the principal. For 2 years at 8%, the amount factor is (1 + 8 / 100)^2 = 1.08^2 = 1.1664. So A = 1.1664 * P. Compound interest CI = A - P = 1.1664 * P - P = 0.1664 * P. We are given CI = Rs 2828.80, so 0.1664 * P = 2828.80. Therefore P = 2828.80 / 0.1664 = Rs 17000. Total amount A = P + CI = 17000 + 2828.80 = Rs 19828.80.

Verification / Alternative Check:
Check using the amount formula directly. A = 17000 * (1.08)^2 = 17000 * 1.1664 = Rs 19828.80. This matches the earlier calculation, confirming that the total amount is correct.

Why Other Options Are Wrong:
Rs. 11828.80 is too low and would imply a negative or very small principal. Rs. 9828.80 is less than the interest itself, so it is not possible as a total amount. Rs. 19328.80 is close but does not match the exact amount obtained from correct calculations.

Common Pitfalls:
A common mistake is to treat compound interest like simple interest and assume CI = P * r * t / 100, which is not valid for compounding. Another error is to forget that CI given is for 2 years and to incorrectly divide it by 2, which is not needed here. Students may also compute the amount factor wrongly by squaring 8 instead of 1.08.

Final Answer:
The correct total amount received by Sunil at the end of 2 years is Rs. 19828.80.