Calculating Compound Interest Rates The nominal rate is the rate of interest with no compounding being taken into consideration. For example, 8 per cent compounded monthly would be considered a nominal rate. The effective annual interest rate (or annual percentage yield) is the rate of interest after compounding has been taken into consideration. Calculating Effective Annual Interest Rate The above formula is used for calculating the effective annual interest rate from a compounded rate. This formula is used in the Annual Interest Rate calculator and in Section One of the Interest Rate Converter. How about an example? 8 per cent interest compounded semi-annually equals what effective annual interest rate? Annual Rate = (1 + [.08 ÷ 2])2 -1 Annual Rate = (1 + .04)2 -1 Annual Rate = 1.0816 -1 Annual Rate = .0816 which equals 8.16 per cent. You probably have concluded that: n = 4 for quarterly compounded interest n = 12 for monthly compounded interest and n = 365 for daily compounded interest. As for calculating continuously compounded interest, we need a new formula (see below) and we must use the mathematical constant e which equals 2.71828182845904523536.... So, let's comptue the effective annual interest rate for a continuously compounded rate of 8 per cent. effective annual interest rate = er -1 effective annual interest rate = (2.71828...).08-1 effective annual interest rate = 1.08328723838081 -1 effective annual interest rate = .08328723838081 effective annual interest rate = 8.328723838081% Calculating the Nominal Rate from an Effective Annual Interest Rate This is the formula used in Section Two of the Interest Rate Converter. If we have an earned annual rate of .08299950680751 (or 8.299950680751%) from an account that was compounded monthly, what was the rate before compounding?Since we are dealing with monthly compounding, n=12. Putting the numbers into the formula, we see that the nominal rate equals: 12 * [(1 + .08299950680751)(1 ÷ 12)-1)] = 12 * [(1.08299950680751)(.08333333...)-1)] = 12 * (1.0066666666666... -1) = 12 * (0.0066666666666) nominal rate = .08 or 8 per cent Once again, we need a special formula when dealing with continuously compounded interest. A bank account yields 9% interest when compounded continuously. What is the nominal interest rate? nominal rate = natural log [1 + .09] nominal rate = 0.0861776962410524 rate = 8.61776962410524% before compounding