## Definition

The term effective interest rate is used to describe the actual rate of interest received when compounding is applied to a nominal rate of interest. The effective interest rate is useful when evaluating alternatives involving various nominal rates applied to different compounding periods.

### Calculation

Effective Interest Rate = (1 + Rate / N)^{N x T} - 1

Where:

- N = number of times the rate is compounded each time period
- T = total number of time periods
- R = rate expressed in decimal form

### Explanation

Also known as effective yield and effective annual interest rate, this is a measure of the rate of interest earned on a loan, or bank deposit, when compounding is applied to the nominal (stated) interest rate.

Compounding takes an interest rate and applies it multiple times in the same period. In doing so, it applies the interest rate to both the principal as well as the growth in principal. When compounding is applied, the effective rate of interest paid will always be higher than the nominal rate applied.

The annual interest rate is useful when comparing loans that offer differing compounding periods (for example, semi-annual, quarterly, and monthly) in addition to differing nominal rates. The effective interest rate should not be confused with the legal term Annual Percentage Rate, which also takes into consideration fees and other costs associated with a loan.

This website offers a compound interest calculator that applies the above concepts to nominal interest rates, and provides semi-annual, quarterly, monthly, weekly and daily results.

### Example

Lindsey is comparing two offers from local banks. First Federal is offering an annual interest rate of 7.20%, while Second National Bank is offering a rate of 7.00% with daily compounding. To make a fair comparison, the Second National Bank needs to be converted into an effective yield.

= (1 + 0.07 / 365)^{365} - 1

= (1 + 0.000192)^{365} - 1

= (1.000192)^{365} - 1

= 1.07250 - 1, or 0.0725

The effective annual interest rate offered by Second National Bank is 0.0725 or 7.25%, which is higher than the offer from First Federal of 7.20%.

### Related Terms

simple interest, compound interest, annual percentage rate, principal, future value