How this calculator works
Annual percentage yield (APY) and annual percentage rate (APR) both describe an annual interest rate, but APY accounts for the effect of compounding within the year while APR (as used here) does not. Two accounts advertising the same nominal rate can pay different amounts depending on how often interest compounds, which is why banks are required to disclose APY for savings products.
This calculator converts in either direction: give it an APR and a compounding frequency to see the equivalent APY, or give it an APY to back out the nominal APR at a chosen compounding frequency. Converting there and back at the same frequency returns the original number, since the two formulas are exact inverses.
The formulas
APY = (1 + r/n)^n − 1APR = n × ((1 + APY)^(1/n) − 1)r is the nominal annual rate as a decimal and n is the number of compounding periods per year (1 for annual, 4 quarterly, 12 monthly, 365 daily). With annual compounding (n = 1), APY and APR are always identical.
Worked example: 5% APR compounded monthly
- Nominal rate r = 0.05, compounding periods n = 12.
- Periodic rate per month = 0.05 ÷ 12 = 0.0041667.
- APY = (1.0041667)^12 − 1 = 0.051162, or 5.1162%.
- A $10,000 balance held for one year earns $511.62 at 5.1162% APY, versus $500 if interest were credited only once a year at the nominal 5% rate.
Frequently asked questions
Why is APY always higher than APR for the same account?
Because APY includes the effect of interest earning interest within the year. The only exception is annual compounding, where interest is credited just once a year and APY equals APR exactly.
Does compounding frequency matter much in practice?
Less than most people expect. Going from monthly to daily compounding at 5% only raises the APY from about 5.116% to roughly 5.127% — a small difference compared to the gap between different nominal rates.
Which number should I compare when shopping for a savings account?
Compare APY, not APR, since APY already accounts for compounding and lets you compare accounts with different compounding schedules on equal terms.
Is APY the same as the interest rate used for a loan?
No — loans are typically quoted and disclosed using APR, which can also include certain fees. APY is the metric used for deposit accounts like savings accounts and certificates of deposit.
How do I convert an APY back to the nominal APR?
Use the formula APR = n × ((1 + APY)^(1/n) − 1), where APY is entered as a decimal and n is the number of compounding periods per year. This is the exact inverse of the APY formula, so converting an APR to APY and then converting that APY back to APR at the same compounding frequency returns the original rate.