Difficulty: Easy
Correct Answer: Rs. 8,820
Explanation:
Introduction:
This is a direct compound interest amount calculation. Albert puts his money into a fixed deposit with compounding once per year, and we need to calculate the maturity amount after 2 years using the standard compound interest formula.
Given Data / Assumptions:
Principal P = Rs. 8,000. Rate r = 5% per annum. Time t = 2 years. Compounding is annual.
Concept / Approach:
For compound interest with annual compounding, the amount after t years is: A = P * (1 + r/100)^t. We substitute P = 8,000, r = 5, and t = 2 to get the maturity amount. The compound interest itself would be A − P, but the question specifically asks for the total amount Albert receives on maturity.
Step-by-Step Solution:
Step 1: Determine the yearly multiplier. 1 + r/100 = 1 + 5/100 = 1.05. Step 2: Compute the square for 2 years. (1.05)^2 = 1.1025. Step 3: Compute the amount A. A = 8000 * 1.1025. A = 8000 * (1 + 0.1025) = 8000 + 8000 * 0.1025. 8000 * 0.1025 = 820. So A = 8000 + 820 = Rs. 8,820.
Verification / Alternative check:
We can also compute year by year. After 1 year, amount = 8000 * 1.05 = 8,400. After the second year, interest is 5% of 8,400 which is 420. So final amount = 8,400 + 420 = Rs. 8,820. This matches the earlier result from the formula.
Why Other Options Are Wrong:
Rs. 8,600 and Rs. 8,500 underestimate the effect of compounding and align more with incorrect simple interest style calculations. Rs. 8,830 brings in a small computational error on the percentage multiplication. Rs. 9,000 is too large and does not correspond to 5% for only 2 years.
Common Pitfalls:
Some learners may accidentally compute simple interest for 2 years and then add it to the principal, missing the second year interest on the increased amount. Others may square the rate incorrectly or misplace a decimal when calculating 1.05 squared. Double checking every step avoids these errors.
Final Answer:
On maturity, Albert will receive a total of Rs. 8,820.
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