# Effective Annual Rate (EAR) Calculator

## Calculator Use

The effective annual rate calculator is an easy way to restate an interest rate on a loan as an interest rate that is compounded annually. You can use the effective annual rate (EAR) calculator to compare the annual effective interest among loans with different nominal interest rates and/or different compounding intervals such as monthly, quarterly or daily. Effective annual rate (EAR), is also called the effective annual interest rate or the annual equivalent rate (AER).

## Effective Annual Rate Formula

\[ i = \left(1+\frac{r}{m}\right)^{m}-1 \]Where r = R/100 and i = I/100; r and i are interest rates in decimal form. m is the number of compounding periods per year. The effective annual rate is the actual interest rate for a year.

With continuous compounding the effective annual rate calculator uses the formula:

\[ i = e^{r}-1 \]- Annual Interest Rate (R)
- is the nominal interest rate or "stated rate" in percent. In the formula, r = R/100.
- Compounding Periods (m)
- is the number of times compounding will occur during a period.
- Continuous Compounding
- is when the frequency of compounding (m) is increased up to infinity. Enter c, C or Continuous for m.
- Effective Annual Rate (I)
- is the effective annual interest rate, or "effective rate". In the formula, i = I/100.

## Effective Annual Rate Calculation:

Suppose you are comparing loans from 2 different financial institutions. The first offers you 7.24% compounded quarterly while the second offers you a lower rate of 7.18% but compounds interest weekly. Without considering any other fees at this time, which is the better terms? Using the effective annual rate calculator you can find the following.

At 7.24% compounded 4 times per year the effective annual rate calculated is

\[ i = \left(1+\frac{r}{m}\right)^{m}-1 \] \[ i = \left(1+\frac{0.0724}{4}\right)^{4}-1 \] \[ i = 0.074389 \]multiplying by 100 to convert to a percentage and rounding to 3 decimal places **I = 7.439%**

At 7.18% compounded 52 times per year the effective annual rate calculated is

\[ i = \left(1+\frac{r}{m}\right)^{m}-1 \] \[ i = \left(1+\frac{0.0718}{52}\right)^{52}-1 \] \[ i = 0.074387 \]multiplying by 100 to convert to a percentage and rounding to 3 decimal places **I = 7.439%**

So based on nominal interest rate and the compounding per year, the effective rate is essentially the same for both loans.

**Cite this content, page or calculator as:**

Furey, Edward "Effective Annual Rate (EAR) Calculator"; from *http://www.calculatorsoup.com* - Online Calculator Resource.