Formula and Use
The effective annual rate formula calculates the rate of interest for a year based on a nominal rate (i) compounded a number of times a year (m).
The effective annual rate is sometimes abbreviated to EAR and often referred to as the annual equivalent rate or AER.
Excel Function
The Excel EFFECT function can be used instead of the effective annual rate formula, and has the syntax shown below.
EFFECT(i,m)
Effective Annual Rate Formula – Quarterly Compounding
To illustrate, suppose the nominal rate is 9% compounded quarterly, then what is the effective annual rate?
In this case the effective interest rate for the year is calculated using the EAR formula as follows:
Effective annual rate = (1 + i / m )m - 1 i = annual nominal rate = 9% m = compounding periods in a year = 4 Effective annual rate = (1 + 9% / 4 )4 - 1 Effective annual rate = 9.308%
Additionally the same answer can be obtained using the Excel EFFECT function as follows:
Effective annual rate = EFFECT(i,m) i = 9% m = 4 Effective annual rate = EFFECT(9%, 4) Effective annual rate = 9.308%
Effective Annual Rate Formula – Monthly Compounding
Consider now what happens if the nominal rate is 9% compounded monthly, again what is the effective annual rate?
In this case the effective interest rate for the year is calculated using the EAR formula as follows:
Effective annual rate = (1 + i / m )m - 1 i = annual nominal rate = 9% m = compounding periods in a year = 12 Effective annual rate = (1 + 9% / 12 )12 - 1 Effective annual rate = 9.381%
Effective Annual Rate Formula – Daily Compounding
Finally suppose the nominal rate is 9% compounded daily, what is the effective annual rate?
In this case the effective interest rate for the year is calculated using the EAR formula as follows:
Effective annual rate = (1 + i / m )m - 1 i = annual nominal rate = 9% m = compounding periods in a year = 365 Effective annual rate = (1 + 9% / 365 )365 - 1 Effective annual rate = 9.416%
It is important to realize that in the 3 examples above the nominal rate (9%) is the same in each case. Only the number of compounding periods in a year is changed from quarterly to monthly and finally to daily. As can be seen the effect of increasing the number of compounding periods is to increase the effective annual rate.
| Compounding periods | Quarterly (4) | Monthly (12) | Daily (365) |
| Effective Annual Rate | 9.308% | 9.381% | 9.416% |
The EAR formula is one of many used in time value of money calculations, discover another at the links below.
About the Author
Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a degree from Loughborough University.