Finance
APR vs APY: Conversion Table and Examples
APR is the yearly rate before compounding, APY what you earn after it. The conversion formula, an APR to APY table by compounding frequency, and why a loan APR includes fees.
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Short answer
APR is a yearly rate before compounding; APY is what you actually earn in a year once interest is added to the balance. To convert, APY = (1 + APR ÷ n)^n − 1, where n is the number of compounding periods a year: 5% compounded monthly is an APY of 5.116%, and compounded daily 5.127%. US savings accounts must quote APY (Regulation DD) and loans must quote APR (Regulation Z), and a loan APR also includes fees, so the two numbers answer different questions.
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On this page
APR and APY in one sentence each
- APR (annual percentage rate): the yearly cost of credit. For a card or credit line it is simply the periodic rate times the number of periods in a year, so a 2% monthly rate is a 24% APR (Regulation Z, §1026.14). For an installment loan it also folds in finance charges such as origination fees (§1026.22).
- APY (annual percentage yield): the total interest a deposit earns over a year, as a percentage of the deposit, assuming the interest stays in the account. It reflects the compounding frequency and nothing else; bonuses do not count (Regulation DD, appendix A).
The same pair exists under other names: nominal rate and effective annual rate (EAR or AER in the UK). When both numbers describe the same account, APY is always equal to or higher than APR, and the gap grows with the rate and the compounding frequency.
The conversion formulas
APR to APY
APY = (1 + APR ÷ n)^n − 1
APY to APR
APR = n × ((1 + APY)^(1/n) − 1)
Continuous compounding
APY = e^APR − 1
Use the rates as decimals: 5% is 0.05. n is 1 for yearly compounding, 4 for quarterly, 12 for monthly and 365 for daily.
Worked example
Worked example: 6% compounded monthly
APY = (1 + 0.06 ÷ 12)^12 − 1 = 1.005^12 − 1 = 0.061678 = 6.17%
On $1,000 that is $61.68 of interest in a year. Regulation DD uses exactly this figure in its own example: $61.68 on $1,000 over 365 days is an APY of 6.17%.
APR to APY table by compounding frequency
Swipe sideways to see every column.
| APR | Yearly | Quarterly | Monthly | Daily (365) | Continuous |
|---|---|---|---|---|---|
| 1% | 1.000% | 1.004% | 1.005% | 1.005% | 1.005% |
| 2% | 2.000% | 2.015% | 2.018% | 2.020% | 2.020% |
| 3% | 3.000% | 3.034% | 3.042% | 3.045% | 3.045% |
| 4% | 4.000% | 4.060% | 4.074% | 4.081% | 4.081% |
| 4.5% | 4.500% | 4.577% | 4.594% | 4.602% | 4.603% |
| 5% | 5.000% | 5.095% | 5.116% | 5.127% | 5.127% |
| 6% | 6.000% | 6.136% | 6.168% | 6.183% | 6.184% |
| 8% | 8.000% | 8.243% | 8.300% | 8.328% | 8.329% |
| 10% | 10.000% | 10.381% | 10.471% | 10.516% | 10.517% |
| 12% | 12.000% | 12.551% | 12.683% | 12.747% | 12.750% |
| 15% | 15.000% | 15.865% | 16.075% | 16.180% | 16.183% |
| 18% | 18.000% | 19.252% | 19.562% | 19.716% | 19.722% |
| 20% | 20.000% | 21.551% | 21.939% | 22.134% | 22.140% |
| 24% | 24.000% | 26.248% | 26.824% | 27.115% | 27.125% |
| 30% | 30.000% | 33.547% | 34.489% | 34.969% | 34.986% |
Two things stand out. At savings-account rates the compounding frequency hardly matters: at 4.5% the difference between monthly and daily is under a hundredth of a point. At credit-card rates it matters a lot: a 24% APR compounded daily costs 27.1% a year if the balance is never paid down.
| Quoted APY | APR if compounded monthly | APR if compounded daily |
|---|---|---|
| 1% | 0.995% | 0.995% |
| 2% | 1.982% | 1.980% |
| 3% | 2.960% | 2.956% |
| 4% | 3.928% | 3.922% |
| 4.5% | 4.410% | 4.402% |
| 5% | 4.889% | 4.879% |
| 6% | 5.841% | 5.827% |
Why a loan APR can be far above its interest rate
On a loan, the APR is not a compounding conversion at all. It is the rate that makes the payments you will make worth exactly the money you actually receive. Fees taken at the start shrink what you receive while the payments stay the same, so the APR rises above the note rate.
Worked example
Worked example: $10,000 at 8% with an origination fee
A 36-month loan of $10,000 at 8% a year has a monthly payment of $313.36. With no fee its APR is 8.00%. If the lender deducts a $300 fee, you receive $9,700 but still repay 36 × $313.36, and the APR becomes 10.08%. With a $500 fee it is 11.52%. Spread the same $300 fee over 60 months instead and the APR is 9.30%: the longer the loan, the less a fixed fee adds per year.
Regulation Z treats a disclosed APR as accurate if it is within 1/8 of a percentage point of the correct figure (1/4 for irregular loans), so small differences between lenders’ calculators are normal.
Which number to compare, and when
| You are comparing | Compare | Watch out for |
|---|---|---|
| Savings accounts or CDs | APY | Introductory APYs that drop after a few months; balance tiers |
| Personal loans or mortgages | APR | Two loans with the same APR but different terms still cost different totals |
| Credit cards | APR, then the effective rate if you carry a balance | Daily compounding: 24% APR costs about 27.1% a year on an unpaid balance |
| A savings APY against a loan APR | Convert one first | A 5% APY and a 5% APR are not the same rate |
Common mistake
An APY is not a promise
APY assumes the rate stays the same for a year and that you leave the interest in the account. A variable savings rate can change next month, and withdrawing interest as it is paid gives you the APR, not the APY.
Do the calculation
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See what a rate and compounding frequency do to your balance year by year, with deposits if you make them.
Tools used in this guide
Sources
The figures and rules in this guide come from these documents.
- 12 CFR Part 1030 (Regulation DD), Appendix A: Annual Percentage Yield CalculationElectronic Code of Federal Regulations (eCFR)APY formula, the 365-day basis and the $61.68 on $1,000 example.
- 12 CFR 1026.14: Determination of annual percentage rate (open-end credit)Electronic Code of Federal Regulations (eCFR)APR for cards and credit lines: periodic rate times the number of periods in a year.
- 12 CFR 1026.22: Determination of annual percentage rate (closed-end credit)Electronic Code of Federal Regulations (eCFR)APR as the cost of credit relating amounts and timing; 1/8 and 1/4 point tolerances.
Facts checked
General information, not legal, tax or financial advice. Rules change; check the cited sources for your own case.