An effective rate of interest calculation is the actual cost of a loan. It is the total amount of interest paid on a loan, expressed as a percentage of the principal. Effective annual interest rates incorporate the effects of compounding.
Effective annual interest rates are calculated in the two following ways:
1. Effective Rate = Total Interest Paid / Principal Amount
2. Effective Rate = (1 + i / n)n – 1
For example, using the first formula, if the starting principal amount is $1,000 and the total interest paid over the course of the year is $104.70, then the effective interest rate is 10.47%. So, look at the following calculation:
.1047 = 104.7 / 1000
Using the second formula, if the starting principal amount is $1,000, the nominal annual interest rate is 10%, and the rate is compounded monthly, then the effective annual rate is 10.47%. Look at the following calculation:
.1047 = (1 + .10/12)12 – 1