The formula
- r
- Annual nominal rate
- EAR
- Effective annual rate
- i
- Monthly periodic rate
- 12
- Monthly periods per year
Example: convert 7% annual rate to monthly
For a nominal 7% loan rate:
For a true 7% effective annual return:
Compounding the second monthly rate for 12 months produces exactly 7% for the year.
Why loan calculators usually divide by 12
Most conventional monthly amortization formulas use the stated nominal annual interest rate divided by 12 as the monthly periodic rate. That is the convention behind the standard fixed-payment loan formula.
Why investment calculators can be different
When an input is labeled expected effective annual return, the monthly rate should be the equivalent rate that compounds back to that annual return. That is why (1 + EAR)1/12 − 1 is appropriate.
Nominal APR and APY are not interchangeable
APR generally describes a nominal annualized borrowing rate, while APY or an effective annual rate includes compounding. Always identify the type of annual rate before converting it.
Check the math with a calculator
Enter your own numbers in the matching Power of Interest calculator. The calculator performs the arithmetic while this page explains the formula and assumptions behind it.