The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum is

Let the sum be x.

We know, Amount = Principal (1 + Rate/100)ⁿ

Compound interest = Amount - Principal

CI = x (1 + 4/100)² - x

CI = 51x/625

We know, Simple interest = (P × R × T)/100

SI = (x × 4 × 2)/100 = 2x/25

It is given that CI - SI = 1

⇒ 51x/625 - 2x/25 = 1

⇒ (51x - 50x)/625 = 1

⇒ x = Rs. 625

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