Difficulty: Easy
Correct Answer: Rs. 693.60
Explanation:
Introduction:
This is a straightforward compound interest computation where the principal, rate, time, and compounding frequency are all clearly specified. The goal is to find the interest portion only, not the final amount, after 2 years of annual compounding.
Given Data / Assumptions:
Principal P = Rs. 8,500. Rate r = 4% per annum. Time t = 2 years. Compounding is annual.
Concept / Approach:
The compound amount after 2 years is: A = P * (1 + r/100)^2. The compound interest CI is A − P. We can compute (1.04)^2 and then multiply by 8,500 to find A and subtract the principal.
Step-by-Step Solution:
Step 1: Compute the multiplier. 1 + r/100 = 1 + 4/100 = 1.04. (1.04)^2 = 1.0816. Step 2: Compute the amount A. A = 8500 * 1.0816. 8500 * 0.0816 = 8500 * 816 / 10000 ≈ 693.60. So A ≈ 8500 + 693.60 = Rs. 9,193.60. Step 3: Compound interest. CI = A − P = 9,193.60 − 8,500 = Rs. 693.60.
Verification / Alternative check:
We can do the year by year method. After 1 year, amount = 8500 * 1.04 = 8,840. Interest in the first year = 340. In the second year, interest is 4% of 8,840 which is 353.60. Total interest over 2 years = 340 + 353.60 = Rs. 693.60, which confirms our result.
Why Other Options Are Wrong:
Rs. 639.60 is close but lower, and it typically comes from mistakenly applying simple interest for 2 years at 4%. Rs. 9,139.60 and Rs. 9,193.60 are amounts, not interest; using these as CI misreads the question. Rs. 600 is a rough approximation that does not match precise calculations.
Common Pitfalls:
A common mistake is to stop after computing SI for 2 years and assume it equals CI. Others misinterpret the amount given as the interest. Always distinguish carefully between the total amount and the interest portion, and ensure that compounding is applied year by year when required.
Final Answer:
The total compound interest on the loan for 2 years is Rs. 693.60.
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