APY to APR Calculator
| Compounding | 12% APR becomes | APY needed for 12% |
|---|---|---|
| Annual (1) | 12.0000% APY | 12.0000% APR |
| Quarterly (4) | 12.5509% APY | 11.4949% APR |
| Monthly (12) | 12.6825% APY | 11.3866% APR |
| Daily (365) | 12.7475% APY | 11.3346% APR |
APR and APY are the same rate wearing two outfits: APR is the nominal annual rate, APY is what compounding turns it into by year-end. This calculator converts both directions for any compounding frequency including the continuous limit - because a 12% APR compounded daily is really 12.7475% APY, and that gap is the whole game.
The Reg DD appendix fixes how banks must compute APY for deposit accounts, and the advertising asymmetry follows from the math: savings accounts quote the bigger APY, loans quote the smaller APR.
How to use
- Enter a rate, pick the direction and the compounding frequency - daily, monthly, quarterly, annual or continuous.
- Read the table for the full 12% ladder: the same nominal rate produces APYs from 12.00% to 12.75% purely by compounding speed.
- Remember loan APR also folds in fees under Reg Z - the calculator converts the rate itself, not fee-loaded loan APRs.
Frequently asked questions
Which is bigger, APR or APY?
APY, always - compounding can only add: 12% APR monthly becomes 12.6825% APY. The two meet only at annual compounding, where the formula collapses to identity. This is why banks put APY on deposits (bigger) and APR on loans (smaller) - the flattering number goes on the billboard.
What is continuous compounding?
The mathematical limit as compounding frequency goes to infinity: e^r − 1, with e the base of natural logarithms. At 12% that is 12.7497% APY - only a hair above daily compounding, which is why the daily-vs-continuous argument is academic outside derivatives pricing.
Why does my loan APR include fees but the savings APY does not?
Different regulations: loan APR under Reg Z folds origination fees and points into one comparable rate, while deposit APY under Reg DD counts only interest paid on the deposit. The two APRs you see in life - mortgage APR and credit card APR - are already fee-adjusted per their own rules.
Does the difference matter at realistic rates?
At 5% daily compounding the gap is 12.7 basis points (5.00% APR = 5.13% APY) - small on one year, real over decades. On a 30-year mortgage the fee component of APR swings the number far more than compounding does, which is why mortgage shoppers compare APRs, not notes rates.