APR to APY Converter
Convert a nominal APR to its effective APY, or work backwards — for any compounding frequency.
12% APR compounded monthly (12×/year) = 12.6825% APY.
A 12% APR compounded monthly equals a 12.68% APY. APR is the nominal yearly rate; APY is the effective rate after compounding is counted. Convert forward with APY = (1 + APR ÷ n)^n − 1, and back with APR = n × ((1 + APY)^(1 ÷ n) − 1), where n is the compounding periods per year.
APR vs APY
APR (annual percentage rate) is the nominal yearly rate — the headline number a lender or bank quotes, before compounding is folded in. APY (annual percentage yield), also called the effective annual rate, is what you actually earn or pay once interest is compounded n times a year. Because interest starts earning interest within the year, APY is always at least as large as APR, and the gap widens as the compounding frequency rises. The two are equal only when interest compounds exactly once a year.
APR is the nominal rate as a decimal and n the compounds per year. Reverse it with APR = n × ((1 + APY)^(1 ÷ n) − 1). For continuous compounding, APY = e^APR − 1 and APR = ln(1 + APY).
Worked example
Convert a 12% APR compounded monthly into its APY.
- 1 Write the APR as a decimal. APR = 12% ÷ 100 = 0.12.
- 2 Divide by the compounding frequency n. APR ÷ n = 0.12 ÷ 12 = 0.01, the rate applied each month.
- 3 Raise (1 + APR ÷ n) to the power n. (1.01)^12 ≈ 1.126825.
- 4 Subtract 1 to get the effective yield. 1.126825 − 1 = 0.126825.
- 5 Multiply by 100 for the APY. 0.126825 × 100 ≈ 12.68% APY.
12% APR at different compounding frequencies
Same 12% nominal APR — only the compounding frequency (n) changes. More frequent compounding lifts the effective APY, but the gains shrink toward the continuous limit.
| Compounding | n per year | Effective APY |
|---|---|---|
| Annual | 1 | 12.00% |
| Semi-annual | 2 | 12.36% |
| Quarterly | 4 | 12.55% |
| Monthly | 12 | 12.68% |
| Daily | 365 | 12.747% |
| Continuous | ∞ | 12.750% |
Why APY is higher — and which rate gets quoted
Why APY exceeds APR. Each time interest is added to the balance, the next period’s interest is calculated on a slightly larger amount. That interest-on-interest is exactly the difference between the nominal APR and the effective APY. With no compounding within the year (n = 1) there is nothing extra to earn, so APY = APR; the more often it compounds, the more the two diverge — up to the continuous-compounding ceiling of e^APR − 1.
Which rate is quoted. By convention, deposit products — savings accounts, CDs, money-market accounts — advertise the APY, because the higher effective figure looks more attractive to savers. Loans and credit cards advertise the APR, the lower-looking nominal rate, even though the amount you actually pay tracks the APY. Converting both sides to APY is the only fair way to compare offers with different compounding schedules.