Effective and nominal rate converter
A rate quoted as 12% is only 12% if it compounds once a year. Convert between the nominal rate a lender quotes and the effective annual rate you actually pay, in either direction, and read off the rate per period the other calculators ask for.
The formula, with your numbers in it
EAR = (1 + i / m)^m - 1The same nominal rate at every frequency
One nominal rate, compounded seven different ways. Each extra compounding period adds less than the one before it, so the effective rate climbs quickly at first and then flattens: continuous compounding is the ceiling nothing beats.
| Frequency | Rate per period | Effective annual | Gap over nominal | Gap, to scale |
|---|---|---|---|---|
| Annual | 12.0000% | 12.0000% | 0.0000% | |
| Semi-annual | 6.0000% | 12.3600% | 0.3600% | |
| Quarterly | 3.0000% | 12.5509% | 0.5509% | |
| Monthly | 1.0000% | 12.6825% | 0.6825% | |
| Weekly | 0.2308% | 12.7341% | 0.7341% | |
| Daily | 0.0329% | 12.7475% | 0.7475% | |
| Continuous | None | 12.7497% | 0.7497% |
Bar length is the gap over the nominal rate, drawn against the continuous gap of 0.7497% as the maximum.
Where the rate per period goes
Every other calculator here takes a rate per period, not a rate per year. That is the number this page exists to give you, and using the annual rate in a monthly schedule is the most common way these come out wrong.
- Loan amortisation scheduleTakes the rate per period and a term in periods. A 12% loan compounded monthly is 1% per period over 360 periods, not 12% over 30.
- NPV and IRR calculatorDiscounts each cash flow at the rate per period. Quarterly flows want the quarterly rate, and the IRR it returns is per period too.
- Present value and annuity tablesThe tables are indexed by rate per period and number of periods, which is why a 1% column and 360 rows is the same thing as a 12% loan over 30 years.