Effective Interest Rate Calculator
Convert a nominal rate into the effective annual rate it really pays — the AER, APY or comparison figure.
A nominal rate quoted "per year, compounded monthly" is not the rate you actually earn.
How the effective interest rate calculator works
A nominal rate quoted "per year, compounded monthly" is not the rate you actually earn. 12% compounded monthly earns 12.68% over the year, because each month's interest starts earning too.
The effective annual rate makes rates with different compounding periods comparable, which is exactly why regulators require an effective annual figure on advertised products, under whichever name applies where you are. Two products can quote the same nominal rate and pay meaningfully different amounts.
Continuous compounding is the limit as the periods get infinitely short — eʳ − 1. It is the ceiling no compounding frequency can beat.
Formula: EAR = (1 + r/m)^m − 1; continuous: eʳ − 1
Worked examples
| Inputs | Effective annual rate | Note |
|---|---|---|
| 12% compounded monthly | 12.6825% | 12.6825% effective |
| 12% compounded yearly | 12% | still 12% — nothing to compound |
| 5% compounded daily | 5.1267% | 5.1267% |
FAQFrequently asked questions
What is the effective annual rate?
What a nominal rate actually pays over a year once compounding is counted. 12% compounded monthly is 12.68% effective.
What is the difference between AER, APY and APR?
AER (UK) and APY (US) are the effective rate on savings. APR is the effective rate on borrowing and also includes fees.
Why do regulators require it?
Because two products quoting the same nominal rate can pay different amounts. The effective rate is the only figure that compares them fairly.
What is continuous compounding?
The limit as the compounding period shrinks toward zero: eʳ − 1. It is the most any frequency can produce.
Does more frequent compounding always help?
It always helps the side receiving interest, but with rapidly diminishing returns — daily barely beats monthly.
Where these figures come from
- CFA Institute — Quantitative Methods: The Time Value of Money — the discounting, annuity and IRR conventions used here
- US Federal Reserve — Regulation Z (Truth in Lending), APR calculation — why APR includes fees where a nominal rate does not
- MoneyHelper (UK Government-backed) — the UK's free money guidance service
Last checked: September 2026. These are the standard textbook formulas; the conventions named are those of the CFA Institute curriculum and ISO 80000 usage.