OneTaskBy Tim King · Updated
APR to APY Calculator
Effective Annual Rate for Daily, Monthly, Quarterly or Continuous Compounding
OneTask is free, with no sign-up, and built by one person.
If this tool saved you time, a coffee helps keep new ones coming.
How the APR to APY Calculator works
This APR to APY calculator converts a nominal annual rate into the effective annual yield once compounding is counted, or works backwards from an APY to the APR. Pick how often interest compounds, from daily to continuous, and it shows both rates and the rate per period.
APR to APY calculator formula
APR is the stated yearly rate before compounding. APY is what that rate actually earns or costs over a year once interest is added to the balance n times. The APR to APY calculator uses:
APY = (1 + APR ÷ n)^n − 1
Going the other way, APR = n × ((1 + APY)^(1/n) − 1). For continuous compounding APY = e^APR − 1. The more often interest compounds, the bigger the gap between the two.
Worked example: monthly compounding
A savings account pays 6% APR compounded monthly. The rate per month is 6 ÷ 12 = 0.5%. Over twelve months that gives (1.005)^12 − 1 = 6.168% APY, so 10,000 grows to about 10,616.78 rather than 10,600.
Worked example: APY back to APR
A lender quotes 5% APY with daily compounding. The APR is 365 × ((1.05)^(1/365) − 1) = 4.879%. Knowing how many times a year interest compounds is essential: the same 5% APY needs a different APR for monthly compounding.
APR to APY reference table
APY for APRs from 1% to 25% with monthly, daily and continuous compounding.
| APR | Monthly | Daily | Continuous |
|---|---|---|---|
| 1.0% | 1.005% | 1.005% | 1.005% |
| 2.0% | 2.018% | 2.020% | 2.020% |
| 3.0% | 3.042% | 3.045% | 3.045% |
| 4.0% | 4.074% | 4.081% | 4.081% |
| 5.0% | 5.116% | 5.127% | 5.127% |
| 6.0% | 6.168% | 6.183% | 6.184% |
| 7.0% | 7.229% | 7.250% | 7.251% |
| 8.0% | 8.300% | 8.328% | 8.329% |
| 9.0% | 9.381% | 9.416% | 9.417% |
| 10.0% | 10.471% | 10.516% | 10.517% |
| 11.0% | 11.572% | 11.626% | 11.628% |
| 12.0% | 12.683% | 12.747% | 12.750% |
| 13.0% | 13.803% | 13.880% | 13.883% |
| 14.0% | 14.934% | 15.024% | 15.027% |
| 15.0% | 16.075% | 16.180% | 16.183% |
| 16.0% | 17.227% | 17.347% | 17.351% |
| 17.0% | 18.389% | 18.526% | 18.530% |
| 18.0% | 19.562% | 19.716% | 19.722% |
| 19.0% | 20.745% | 20.919% | 20.925% |
| 20.0% | 21.939% | 22.134% | 22.140% |
| 21.0% | 23.144% | 23.360% | 23.368% |
| 22.0% | 24.360% | 24.599% | 24.608% |
| 23.0% | 25.586% | 25.851% | 25.860% |
| 24.0% | 26.824% | 27.115% | 27.125% |
| 25.0% | 28.073% | 28.392% | 28.403% |
Quick answers
- 5% APR compounded monthly is 5.116% APY.
- 12% APR compounded monthly is 12.683% APY.
- With annual compounding APR and APY are the same.
- Daily compounding adds only a little over monthly.
- Continuous compounding gives the highest APY for a given APR.
FAQ
What is the difference between APR and APY?
APR is the simple yearly rate without compounding, and APY is the effective yearly rate including it. Savings products tend to advertise APY because it is higher, while loans often advertise APR because it looks lower.
Does APR include fees?
On many loans the regulated APR also rolls in certain upfront fees, which makes it higher than the note rate. This calculator treats the rate as pure interest, so enter the rate that is compounded and add fees separately if you need them.
Which compounding frequency should I choose?
Use the one in your account or loan terms. Credit cards and many savings accounts compound daily, mortgages usually monthly, and some bonds semi-annually. If the terms don't say, monthly is the most common choice for consumer products.
Is the effective annual rate the same as APY?
Yes. Effective annual rate, EAR and annual equivalent rate all describe the same idea as APY: the rate after a full year of compounding. The names vary between countries and products but the arithmetic is identical.
See also: all Debt tools, Pay, Bills, Property, Investing, Saving.
Related tools
Simple Interest Calculator
Simple interest, total amount and interest per year and month.
Compound Interest Calculator
Growth on a balance, with regular contributions and the real rate.
Future Value Calculator
Future value or present value of money at any rate.
Loan Comparison Calculator
Compare two loans by payment, interest, fees and total cost.
Savings Goal Calculator
The weekly, fortnightly or monthly amount that reaches a savings target on time.