If the compound interest (compounded Yearly) on a certain sum for 2 years at…

Concept: For a sum invested at rate R% per annum compounded annually, the compound interest over t years is CI = P[(1 + R/100)t − 1], while the simple interest over the same principal, rate, and time is SI = P·R·t/100. Because both formulas share the same principal, rate, and time, a CI value can be used to back-solve for the principal, and that principal can then be substituted into the simple-interest formula to get the corresponding SI.

Application:

1. Compute the compounding factor for R = 3% over t = 2 years: (1 + 3/100)2 = (1.03)2 = 1.0609.

2. Write the CI equation: CI = P(1.0609 − 1) = P × 0.0609.

3. Substitute the given CI = Rs. 101.50 and solve for P: P = 101.50 ÷ 0.0609 = Rs. 1666.67 (= 5000/3).

4. Apply the simple-interest formula with this principal for the same rate and time: SI = P × R × t ÷ 100 = 1666.67 × 3 × 2 ÷ 100 = Rs. 100.00.

Cross-check: for exactly 2 years, CI and SI on the same sum are related by CI − SI = P·(R/100)2, so SI = CI ÷ (1 + R/200). Substituting R = 3% and CI = 101.50 gives SI = 101.50 ÷ 1.015 = Rs. 100.00 — confirming the value obtained above without needing to separately verify P.