The simple interest on a certain principal at 7% per annum for 4 years is Rs 2415. Using this information, what will be the compound interest on the same principal at 4% per annum, compounded annually, for a period of 2 years?

Introduction / Context:
This problem mixes simple interest and compound interest. First, it gives the simple interest on a principal at 7% per annum for 4 years. From that, we must deduce the principal. Then we are asked to compute the compound interest on the same principal at a different rate of 4% per annum for 2 years. This tests your ability to connect the two interest concepts and move between them accurately.

Given Data / Assumptions:

• Simple interest SI = Rs 2415.
• Rate for SI r1 = 7% per annum.
• Time for SI t1 = 4 years.
• Rate for CI r2 = 4% per annum.
• Time for CI t2 = 2 years.
• Compounding is annual for the compound interest part.

Concept / Approach:
Simple interest is given by:
SI = P * r1 * t1 / 100 From this we can find the principal P. Then for compound interest, the amount after t2 years at rate r2 is:
A = P * (1 + r2 / 100)^t2 The compound interest CI is:
CI = A - P

Step-by-Step Solution:
Use SI formula: 2415 = P * 7 * 4 / 100. So 2415 = P * 28 / 100. Therefore P = 2415 * 100 / 28. Compute P = 241500 / 28 = Rs 8625. Now compute compound interest for 2 years at 4%. Amount factor for 2 years: (1.04)^2 = 1.0816. Amount A = 8625 * 1.0816. A = Rs 933, take care to compute accurately: 8625 * 1.0816 = Rs 933 - this is shorthand, but the difference from principal is what matters. Compound interest CI = P * (1.04^2 - 1) = 8625 * 0.0816. CI = 8625 * 0.0816 = Rs 703.8, which rounds to Rs 704.

Verification / Alternative Check:
You can compute A explicitly: A = 8625 * 1.0816 ≈ 9328.8. Then CI = A - P = 9328.8 - 8625 = 703.8, which again rounds to Rs 704. Thus the chosen option 704 is consistent with both methods.

Why Other Options Are Wrong:
Rs. 854 and Rs. 893 are significantly larger than the correct interest and correspond to higher effective rates than 4% over 2 years. Rs. 914 is even larger and not supported by the compound interest formula with the given data.

Common Pitfalls:
Some learners mistakenly compute simple interest on 8625 at 4% for 2 years, ignoring compounding, which gives a slightly lower value. Another frequent error is miscalculating the principal from the simple interest equation. Rounding too early during calculations can also cause small mismatches, so it is better to round only at the end.

Final Answer:
The correct compound interest for 2 years at 4% per annum is Rs. 704.