On Equation Finance Calculator Effective Annual Rates formula for calculating the Effective Annual Rates

What is the Effective Annual Rate?

The Effective Annual Rate (EAR) is the rate of interest actually earned on an investment as a result of compound interest over a period of time. It Effective Annual Rate is usually higher than the nominal rate and is used to compare different financial products that calculate annual interest with different compounding periods – weekly, monthly, yearly, etc. Increasing the number of compounding periods makes the effective annual interest rate increase as time goes by.


Effective Annual Rate Variables

The Effective Annual Rate is calculated by taking the nominal rate and adjusting it to account for periodic compound interest effects over the course of a year. The variables for the Effective Annual Rate are as follows:

Nominal Rate of Interest (i)

Nominal Rate of Interest is the stated or given annual rate of interest that does not account for compound interest of multiple periodic payments.

Number of Payments per Year (n)

The Number of payments during a year in which the interest is compounded.

Effective Annual Rate of Interest (r)

The Effective Annual Rate of Interest (EAR) is the adjusted annual rate or real rate of interest paid on an investment or loan over the course of a year.


How to Calculate Effective Annual Rates

The Effective Annual Rate is calculated in the following way, where r is the effective annual rate, i the nominal rate, and n the number of compounding periods per year. If an investment or loan has a nominal rate of 12% (i = 0.12) compounded monthly (n = 12), the calculation of the Effective Annual Rate is as follows:

r = (1+( i/n ))n -1

r = (1+( 0.12/12 ))12 -1

r = 0.1268 = 12.68%

In this example, the Effective Annual Rate for a nominal 12% rate compounded over 12 months is 12.68%. This is 0.68% higher than the nominal rate after adjusting for compound interest effects of monthly interest paid.


On Equation Finance Calculator example of how to calculate Effective Annual Rates with the On Equation Finance Calculator App

Advantages of the EAR

The primary advantage of using the Effective Annual Rate is simply that it is a more accurate figure of actual interest earned on a financial instrument or investment, or of actual interest paid on a loan, such as a home mortgage.

The Effective Annual Rate calculation is commonly used to value bonds on the bond market. It provides the real interest rate returned in a given time period, based on the actual book value of a financial instrument at the beginning of the time period. If the book value of the investment declines, then the actual interest earned will decline as well.


Effective Annual Rate Summary

The Effective Annual Rate (EAR) is the actual rate which the investor earns on investments or pays to a financial institution in which they have borrowed money from. It is dependent upon the number of compounding periods and the nominal rate of interest. The Effective annual rate of interest increases if the number of compounding periods increases for the same nominal rate.


On Equation Finance Calculator App Screen example of Effective Annual Rates with no values loaded in calculator inputs

Effective Annual Rates with On Equation Finance Calculator

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