APR against APY on the same rate
APR is a nominal annual rate: the periodic rate multiplied by the number of periods, with the compounding left out. APY, or AER on a savings account, folds the compounding back in. At 12% compounded monthly the periodic rate is 1% and the effective rate is 12.68%, because each month's interest earns interest for the rest of the year. The gap widens with the rate: at 24% nominal it is nearly three percentage points.
The same nominal rate, compounded differently
| Annually | 1 | 12.00% | 12.00% |
| Half-yearly | 2 | 6.00% | 12.36% |
| Quarterly | 4 | 3.00% | 12.55% |
| Monthly | 12 | 1.00% | 12.68% |
| Weekly | 52 | 0.23% | 12.73% |
| Daily | 365 | 0.03% | 12.75% |
| Continuously | 0 | 0.00% | 12.75% |
An estimate, not financial advice. Figures are illustrative and depend on assumptions listed below. Check anything you plan to act on with a qualified adviser or the provider itself.
The same nominal rate, compounded more and more often. Nearly all of the gain arrives by monthly; the rest is a rounding error chasing a limit.
Nominal rates are comparable only at the same compounding frequency. Effective rates are always comparable.
The gap grows with the square of the rate, roughly, so it is negligible at 2% and substantial at 25%.
Lenders often quote nominal and savings providers often quote effective, which flatters both.
How it works
The formula
From a nominal rate to the effective one:
effective = (1 + nominal/n)^n - 1
And back again:
nominal = n x ((1 + effective)^(1/n) - 1)
Continuously compounded, the limit as n grows:
effective = e^nominal - 1
nominal = ln(1 + effective)
n = periods a year: 1, 2, 4, 12, 52, 365
The two directions are exact inverses, which is
asserted rather than assumed.
What it assumes
- The nominal rate is the periodic rate multiplied by the number of periods, which is what a nominal rate means and what almost every lender quotes.
- Nothing here includes fees. A regulatory APR in most jurisdictions folds compulsory charges into the figure as well as the compounding, so a legal APR and the effective rate computed here are not always the same number.
- Continuous compounding is a limit rather than a frequency, so it has no period and therefore no per-period rate. Reporting the instantaneous rate under that label would be a different quantity wearing the same name.
- The rate is constant for the year. A variable rate has no single effective figure.
- Nothing on this page is denominated in a currency, because a rate conversion is identical everywhere. That is why there are no money fields and no currency symbols.
Common questions
Which figure is on my credit card statement?
Usually a nominal APR, converted to a monthly rate for the statement itself. The interest you actually pay over a year on a balance you never clear is the effective rate, which is higher — 22.9% nominal compounded monthly is about 25.5% effective. The disclosure rules differ by country and some jurisdictions require the compounded figure.
Why do savings accounts quote AER?
Because it is the comparable figure, and requiring it stops a provider making a monthly-compounded account look identical to an annual one. AER is the effective annual rate under a different name. Comparing a nominal rate against an AER understates the first, which is why the direction of this tool matters when reading two offers side by side.
Sources
Method written and checked by Tessalor on Jul 31, 2026.
The full method, worked example and every assumption behind this figure are on APR and APY Calculator.