The simple interest accrued on a sum of ₹ 20000 in 3 years is ₹ 7200. What…

Simple interest (SI) is worked out only on the original principal every year, so SI = P × R × T / 100 stays proportional to time. Compound interest (CI), by contrast, is worked out on the principal plus every interest amount already added in earlier periods, so for annual compounding CI = P × [(1 + R/100)T − 1]. Because interest starts earning interest of its own from the second period onward, CI is always greater than SI for the same P, R and T once T is more than 1 year, and the gap between them widens as time passes.

1. Find the rate R from the given simple interest: R = (SI × 100) / (P × T) = (7200 × 100) / (20000 × 3) = 720000 / 60000 = 12% per annum.

2. Write the amount after 3 years of annual compounding at this rate: A = P × (1 + R/100)3 = 20000 × (1.12)3.

3. Evaluate the power: (1.12)3 = 1.12 × 1.12 × 1.12 = 1.404928.

4. So the amount A = 20000 × 1.404928 = ₹28098.56.

5. Compound interest = Amount − Principal = ₹28098.56 − ₹20000 = ₹8098.56.

Independent check using the standard shortcut for the CI−SI gap over 3 years, CI − SI = P × R2 × (300 + R) / 106: with P = 20000 and R = 12, this gives 20000 × 144 × 312 / 1,000,000 = ₹898.56, so CI = ₹7200 + ₹898.56 = ₹8098.56 — matching the direct computation above.