Difficulty: Easy
Correct Answer: Rs. 612
Explanation:
Introduction / Context:
This is a straightforward computation of compound interest for a given principal, rate and time with annual compounding. You simply apply the compound interest formula, then subtract the principal to find the interest earned.
Given Data / Assumptions:
Concept / Approach:
For annual compounding: Amount A = P * (1 + r/100)^t. Compound interest: CI = A − P. We first compute the amount factor (1 + 4/100)^2, multiply it by the principal to get A, and then subtract P to obtain CI.
Step-by-Step Solution:
Step 1: Compute the yearly factor. 1 + r/100 = 1 + 4/100 = 1.04. Step 2: Apply the factor for 2 years. (1.04)^2 = 1.04 * 1.04 = 1.0816. Step 3: Compute the amount A. A = 7,500 * 1.0816 = Rs. 8,112. Step 4: Compute the compound interest. CI = A − P = 8,112 − 7,500 = Rs. 612.
Verification / Alternative check:
Compute year by year. Year 1: interest = 7,500 * 4% = 300; amount = 7,500 + 300 = 7,800. Year 2: interest = 7,800 * 4% = 312; amount at end of year 2 = 7,800 + 312 = 8,112. Total interest = 300 + 312 = 612, confirming the earlier result.
Why Other Options Are Wrong:
Values such as 512, 515 and 522 are all below the true compound interest of 612. They may arise if someone mistakenly computes simple interest (which would give 7,500 * 4 * 2 / 100 = 600) and then adjusts slightly, but they do not match the exact result from correct compounding.
Common Pitfalls:
Some students forget to apply the interest on the increased amount in the second year and simply double the first year's interest. Others round too early in the calculation. It is important to either use the formula directly or compute interest year by year carefully.
Final Answer:
The compound interest on Rs. 7,500 for 2 years at 4% per annum is Rs. 612.
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