Simple interest on a certain principal at 7% per annum for 4 years is Rs. 2,415. Using this information to find the principal, what will be the compound interest on the same principal at 4% per annum for 2 years, compounded annually?

Introduction:
This problem links simple interest and compound interest. We first use the given simple interest to determine the unknown principal, and then we use that principal to compute compound interest at a different rate and time. It nicely checks understanding of both formulas in one question.

Given Data / Assumptions:
Simple interest SI = Rs. 2,415. Simple interest rate = 7% per annum. Simple interest time = 4 years. For compound interest: rate = 4% per annum, time = 2 years, compounded annually.

Concept / Approach:
First, use the simple interest formula: SI = P * r * t / 100. From this, find the principal P. Then apply the compound interest amount formula for 2 years: A = P * (1 + r/100)^2, and compute compound interest as CI = A − P.

Step-by-Step Solution:
Step 1: Find the principal using SI. 2415 = P * 7 * 4 / 100. 2415 = P * 28 / 100. P = 2415 * 100 / 28 = 241500 / 28 = Rs. 8,625. Step 2: Apply compound interest for 2 years at 4%. Amount A = 8625 * (1.04)^2. (1.04)^2 = 1.0816. A = 8625 * 1.0816 ≈ Rs. 9,328.80. Step 3: Compound interest. CI = A − P ≈ 9,328.80 − 8,625 = Rs. 703.80. Rounded to the nearest rupee, CI ≈ Rs. 704.

Verification / Alternative check:
Instead of computing the full amount, we can directly compute: CI = P * [(1.04)^2 − 1] = 8625 * 0.0816. 8625 * 0.0816 ≈ 8625 * 816 / 10000 ≈ Rs. 703.8, which again confirms about Rs. 704.

Why Other Options Are Wrong:
Rs. 854, Rs. 893, Rs. 914, and Rs. 678 all come from incorrect principal calculations or wrong handling of the compound interest formula. Many of them result from using simple interest instead of compound interest or misusing the percentage value.

Common Pitfalls:
Learners often forget to first compute the principal from the given simple interest data and instead try to mix both rates directly. Another common mistake is to apply the simple interest formula again for the second part, which will not give the correct compound interest value.

Final Answer:
The compound interest on the same principal at 4% per annum for 2 years is approximately Rs. 704.