The difference of compound interest and simple interest on a sum of money at the rate of 5% per year for 2 years is 250. The sum is

To find the principal sum when the difference between compound interest (CI) and simple interest (SI) for 2 years is given, we use the standard formula: Difference = P(r/100)^2. Simple interest is calculated only on the initial principal, while compound interest is calculated on both the principal and the accumulated interest from previous periods. For a 2-year period, the difference arises specifically from the interest earned on the first year's interest. Given the rate (r) is 5% and the difference is 250, the equation becomes 250 = P(5/100)^2. Simplifying this, 250 = P(1/20)^2, which leads to 250 = P/400. Multiplying 250 by 400 results in a principal (P) of 1,00,000. This mathematical relationship demonstrates how compounding grows exponentially compared to the consistent growth of simple interest.

Sources

1. [1] https://www.investopedia.com/articles/investing/020614/learn-simple-and-compound-interest.asp