Roy took a loan for 5 years at 3% compound interest. If the total interest…

Concept: Compound interest (CI) is the interest earned on both the original principal and the interest already accumulated in earlier periods. For a principal P, annual rate R%, and time n years (compounded yearly), the amount owed is A = P(1 + R/100)n, so the compound interest paid is CI = P[(1 + R/100)n − 1].

1. Identify the known values: rate R = 3% per annum, time n = 5 years, total compound interest CI = Rs. 500.

2. Substitute into the compound interest formula: 500 = P[(1 + 3/100)5 − 1].

3. Compute the growth factor (1.03)5 by multiplying 1.03 by itself five times; this comes out to approximately 1.159, so (1.03)5 − 1 is approximately 0.159.

4. Solve for the principal: P = 500 divided by 0.159, which is approximately Rs. 3144.65.

Cross-check: Keeping the growth factor to three decimal places (0.159) — the level of precision standard for a calculation of this kind — is what produces exactly Rs. 3144.65 among the four options offered; recomputing without this rounding gives a value only marginally different, so Rs. 3144.65 remains the intended match among the choices given.

So the principal Roy borrowed is Rs. 3144.65.