What is the formula for calculating effective interest rate?

The formula for calculating the effective interest rate is derived from the nominal interest rate and the number of compounding periods in a year. The effective interest rate gives a clearer picture of the actual cost of borrowing or the actual return on an investment when compounding is taken into account.

The selected answer is based on the equation for converting a nominal annual interest rate (i) into an effective interest rate, with m representing the number of compounding periods per year. The expression (1 + [i/m])^m - 1 effectively captures the impact of compounding: it calculates the interest accrued over multiple periods rather than just applying the nominal rate linearly.

By dividing the nominal rate, i, by the number of compounding periods, m, you obtain the interest rate applied to each compounding period. Raising this sum to the power of m accounts for the effect of compounding over the year, and subtracting 1 results in the effective interest rate.

This formula allows individuals and financial professionals to compare different interest rates that may have varying compounding structures and find the true cost of borrowing or investment returns accurately.