The difference between simple and compound interest compounded annually on a certain sum for 2 years at 4% p.a. is Re. 1. Find the sum.

Problem restatementFor two years at rate r, the excess of CI over SI equals P r². Use this to get P.

Given data

• r = 4% = 0.04; CI − SI = Re. 1

Step-by-step calculationP r² = 1 ⇒ P × (0.04)² = 1P × 0.0016 = 1 ⇒ P = 625

Verification/AlternativeWith P = 625: SI (2 yrs) = 625 × 0.08 = 50; CI = 625[(1.04)² − 1] = 625(0.0816) = 51; difference = 1.

Common pitfallsApplying the identity for periods other than exactly 2 years.

Final AnswerRs. 625