APR to APY Calculator
Turn an APR into the APY you actually earn or pay, or the other way around.
Good to know. Banks quote APY on savings and APR on loans. Both are true, and each is the flattering one.
Not financial advice. Uses only the numbers and rates you enter — no live data.
How it works
In plain words
Divide the APR by the number of times interest is added in a year, grow 1 by that rate once for each time, and take away 1. For APY to APR, reverse the steps.
The formula
APY = (1 + APR ÷ n)ⁿ − 1 APR = n × ((1 + APY)^(1/n) − 1) continuous: APY = e^APR − 1
Worked example
5% APR compounded monthly is 5% ÷ 12 = 0.4167% a month. Over 12 months, (1 + 0.05 ÷ 12)¹² − 1 = 5.116% APY: 511.62 of interest on 10,000.
Sources
- Brealey, Myers and Allen, Principles of Corporate Finance, chapter 2 The standard formulas for loan payments, compounding and present value, the same as a spreadsheet’s PMT and FV.
- Regulation DD (Truth in Savings), Appendix A: Annual Percentage Yield Calculation How US banks must work out and show the APY.
Sources checked September 30, 2026. 3 automated tests check its answers on every change.
About the APR to APY calculator
An APR, or annual percentage rate, is the yearly rate before compounding. An APY, or annual percentage yield, includes the effect of interest earning interest during the year. When interest is added monthly or daily, the APY is higher than the APR, and it is what you actually earn or pay over a year.
Savings accounts and CDs in the US must advertise the APY, under the Truth in Savings Act, so you can compare accounts that compound differently. Loans and credit cards advertise the APR, which looks lower. A credit card at 24% APR compounded daily costs 27.1% a year if the balance is never paid down.
The more often interest compounds, the bigger the gap, but it levels off quickly: 5% compounded daily is 5.127%, only a little more than monthly (5.116%), and continuous compounding is the upper limit (5.127%).
For a mortgage or car loan, the official APR also includes fees, so it is higher than the plain interest rate. This converter treats the APR as a plain annual rate. In the UK and Europe, the effective rate on savings is often called AER, and on loans APR already means the effective yearly cost including fees.
Questions people ask
What is 5% APR as APY?
5.116% if interest compounds monthly, 5.127% if daily, and 5% if it is added once a year.
What is the difference between APR and APY?
APR is the yearly rate without compounding. APY includes compounding, so it shows what you really earn or pay in a year.
Is a higher APY better?
On savings, yes: it is what you earn. On a loan, the effective rate is what you pay, so lower is better.
How do I convert APY to APR?
Take the n-th root of 1 + APY, subtract 1 and multiply by n, the number of compounding periods a year. 5.116% APY monthly is 5% APR.