How to calculate the effective annual interest rate (EAR)
About this lesson
In this video, I will explain the effective annual interest rate and its calculation with a numerical example.
APR vs EAR
Interest rates are usually quoted as an annual percentage rate (APR), without compounding. When interest is added more than once a year, you earn interest on interest, so the true yearly rate, the effective annual rate (EAR), is higher.
The formula
EAR = (1 + APR ÷ m)m − 1
where m is the number of compounding periods per year.
Example: 12% APR
| Compounding | m | EAR |
|---|---|---|
| Annually | 1 | 12.00% |
| Semi-annually | 2 | 12.36% |
| Quarterly | 4 | 12.55% |
| Monthly | 12 | 12.68% |
| Daily | 365 | 12.75% |
| Continuously | — | 12.75% |
Monthly: (1 + 0.12 ÷ 12)12 − 1 = 1.0112 − 1 = 12.68%
Continuous compounding
As compounding gets more frequent, the EAR approaches:
EAR = eAPR − 1 → e0.12 − 1 = 12.75%
In Excel
- APR to EAR:
=EFFECT(12%,12)→ 12.68% - EAR to APR:
=NOMINAL(12.68%,12)→ 12%
Why it matters
Use the EAR to compare loans, savings accounts or investments that compound at different frequencies. A 12% loan compounded monthly costs more than a 12% loan compounded once a year.