What is the effective annual rate?
A rate of 5% a year means something different when interest is added monthly, daily or once a year. Type the nominal rate and how often interest is added; the answer is what you really earn in a year.
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Your answer
5% a year, added monthly, is an effective 5.12% a year.
- 5.12%Effective yearly ratewhat 5% becomes when interest is added monthly
- 0.12 pointsMore than the nominal ratepercentage points a year
- 5.13%If added dailyabout the most any frequency can give
Effective rate = (1 + r ÷ n)ⁿ − 1, with n the number of times interest is added each year. Banks call it APY or AER; it ignores fees and tax.
| Interest added | Effective rate |
|---|---|
| Yearly | 5.000% |
| Half-yearly | 5.063% |
| Quarterly | 5.095% |
| Every two months | 5.105% |
| Monthly | 5.116% |
| Twice a month | 5.122% |
| Every two weeks | 5.122% |
| Weekly | 5.125% |
| Twice a week | 5.126% |
| Daily (360-day year) | 5.127% |
| Daily (365 days) | 5.127% |
The investment calculator opens with this rate and compounding, so you can see what a plan grows to.
Illustration only, not investment advice. Assumes a steady return; real returns vary.
Why the frequency matters
When interest is added more than once a year, each addition starts earning interest itself before the year ends. A nominal 5% added monthly is 0.4167% each month, and twelve of those compound to 5.116% over the year.
The gain from compounding more often shrinks quickly: monthly is close to daily, and daily is close to the continuous limit. Yearly versus monthly is the step that matters over decades; monthly versus daily rarely does.
Compare offers on their effective rate, not their nominal one. Two accounts quoting 5% can pay different amounts if one adds interest yearly and the other monthly; the effective rate puts them on the same footing.
Questions and answers
What is the difference between a nominal and an effective rate?
The nominal rate is the yearly figure a bank or fund quotes. The effective rate is what you actually get in a year once interest is added more than once and starts earning on itself. 5% compounded monthly gives 5.12% effective; compounded daily, 5.13%. The gap grows with the rate: 10% monthly is 10.47% effective.
Why does the effective rate matter?
It is the only fair way to compare two offers that compound differently. A 5% rate added quarterly (5.09% effective) beats a 5.05% rate added once a year. The same arithmetic applies to loans, where a quoted rate charged monthly costs more than the same rate charged yearly. The full calculator shows the effective rate under its compounding setting.
What is the formula?
Effective rate = (1 + r ÷ n)^n − 1, where r is the nominal yearly rate and n the number of times interest is added each year. For 5% monthly: (1 + 0.05 ÷ 12)^12 − 1 = 0.0512, or 5.12%. As n grows, the result approaches e^r − 1, so daily and continuous compounding differ by almost nothing.
Is the effective annual rate the same as APY?
Yes. APY, the annual percentage yield, is what US banks call the effective annual rate: 5% compounded monthly is a 5.12% APY. In Europe the same figure is often called AER. A nominal rate quoted as APR leaves the compounding out, so accounts compare fairly on APY or the effective rate.