See Also:

What is Compound Interest

When is Interest Rate Not an Important in Selecting a Loan?

Nominal Interest Rate

Interest Rate Swaps

Fixed Interest Rate vs Floating Interest Rate

# Effective Rate of Interest Calculation

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 Rate Formula

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**

(Where **i** is the nominal rate and **n** is the number of compounding periods per year.)

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

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