The compound interest earned by Sunil on a certain principal amount at the end of 2 years at the rate of 8% per annum (compounded annually) is Rs. 2,828.80. What is the total amount that Sunil receives at the end of 2 years (principal plus interest)?

Introduction / Context:
This question gives you the compound interest earned in 2 years at a known rate and asks for the final amount (principal plus interest). To answer it, you must first recover the principal from the compound interest data, then add the interest back to get the total amount. It combines understanding of compound interest formulas with basic algebra.

Given Data / Assumptions:
- Let the principal be P rupees.
- Compound interest for 2 years at 8% per annum = Rs. 2,828.80.
- Interest is compounded annually.
- Rate r = 8% per annum, time t = 2 years.
- We must find the total amount A = P + C.I. at the end of 2 years.

Concept / Approach:
For 2 years of annual compounding at rate r, the amount is A = P * (1 + r/100)^2. The compound interest is C.I. = A - P = P * ((1 + r/100)^2 - 1). For r = 8%, (1.08)^2 = 1.1664, so the interest factor is 0.1664. Thus C.I. = P * 0.1664. We set this equal to 2,828.80 and solve for P. Then, the amount A is P + 2,828.80.

Step-by-Step Solution:
Step 1: Use C.I. formula for 2 years: C.I. = P * ((1.08)^2 - 1).Step 2: Compute (1.08)^2 = 1.1664, so (1.08)^2 - 1 = 0.1664.Step 3: Therefore, C.I. = P * 0.1664.Step 4: Given C.I. = 2828.80, so P * 0.1664 = 2828.80.Step 5: Solve for P: P = 2828.80 / 0.1664.Step 6: Perform the division: P = 17000.Step 7: Total amount A after 2 years = P + C.I. = 17000 + 2828.80 = 19828.80.Step 8: Hence, Sunil receives Rs. 19,828.80 in total after 2 years.

Verification / Alternative check:
Check by forward computation: Starting from P = 17,000 at 8% per annum for 2 years, amount A = 17000 * (1.08)^2 = 17000 * 1.1664 = 19828.8. Compound interest = A - P = 19828.8 - 17000 = 2828.8, which matches the given C.I. This confirms that both principal and amount are correct.

Why Other Options Are Wrong:
Rs. 11,828.80 and Rs. 9,828.80 are far below the principal plus interest total and might come from subtracting instead of adding the interest. Rs. 19,328.80 and Rs. 17,828.80 correspond to incorrect principal values when using the C.I. relationship. Only Rs. 19,828.80 is consistent with the given interest and the 8% compound growth over 2 years.

Common Pitfalls:
Some learners mistakenly think the given Rs. 2,828.80 is the final amount rather than just the interest, leading to underestimation of the principal. Others forget to square 1.08 for two years or miscompute the decimal 0.1664. Always interpret C.I. as amount minus principal and use exact factors when solving for P and A.

Final Answer:
The total amount that Sunil receives after 2 years is Rs. 19,828.80.