The effective annual interest rate (or annual percentage yield) is the rate of interest after compounding has been taken into consideration.
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 + .04)2 -1
Annual Rate = 1.0816 -1
Annual Rate = .0816 which equals 8.16 per cent.
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)
So, let's comptue the effective annual interest rate for a continuously compounded rate of 8 per cent.
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.
Once again, we need a special formula when dealing with continuously compounded interest.
What is the nominal interest rate?