Suppose a bank gives an interest of 10% per annum compounded annually for a fixed deposit for a period of two years. What should be the simple interest rate per annum if the maturity amount after two years is to remain the same ?

To find the equivalent simple interest rate, we first calculate the maturity amount under compound interest. For a principal P at 10% compounded annually for two years, the amount is A = P(1 + 0.10)² = P(1.21) [1]. This results in a total interest of 0.21P over two years. For simple interest to yield the same maturity amount, the total interest earned must also be 0.21P [2]. The simple interest formula is A = P(1 + rt), where r is the annual rate and t is the time in years. Setting 1 + r(2) = 1.21, we solve for r: 2r = 0.21, which gives r = 0.105 or 10.5% per annum. Thus, a 10.5% simple interest rate is required to match the 10% annual compounding effect over a two-year period.

Sources

1. [1] https://www.investopedia.com/articles/investing/020614/learn-simple-and-compound-interest.asp
2. [2] https://www.investopedia.com/terms/s/simple_interest.asp