If the simple interest on a sum for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same principal, at the same rate, for the same 2 years?

Problem restatement
From SI over 2 years, infer the principal, then compute CI for the same period at the same rate.

Given data

• SI = Rs. 50 on rate r = 5% p.a., time t = 2 years

Concept/Approach
Use SI = P r t to get P. Then CI = P[(1 + r)^t − 1].

Step-by-step calculation
50 = P × 0.05 × 2 ⇒ 50 = 0.10P ⇒ P = Rs. 500CI = 500 × [(1.05)² − 1] = 500 × (1.1025 − 1) = 500 × 0.1025CI = Rs. 51.25

Verification/Alternative
Year-wise: Year 1 interest = 25; Year 2 interest = 25 on P plus 1.25 on previous year's interest = 26.25; total = 51.25.

Common pitfalls
Forgetting that CI includes interest on interest in the second year.