APR vs APY in plain English
APR is a nominal annual rate. APY is the effective annual rate after compounding. If interest compounds more than once per year, APY will be higher than APR (for positive rates).
Conversion formula
APY = (1 + APR/n)^n - 1, where n is compounding periods per year.
How to convert APR to APY (step-by-step)
- Identify compounding frequency (monthly, daily, etc.).
- Convert APR to a periodic rate (APR / n).
- Apply the formula to compute APY.
Quick conversion examples
| APR | Compounds/year | APY (approx) |
|---|---|---|
| 6.0% | 12 (monthly) | ~6.17% |
| 6.0% | 365 (daily) | ~6.18% |
| 12.0% | 12 (monthly) | ~12.68% |
APR vs APY example
At 6% APR compounded monthly, APY is about 6.17% because interest earns interest.
APR/APY for deposits vs loans
- Savings products often advertise APY to standardize yield including compounding.
- Loans often quote APR, but total cost also depends on amortization and fees.
- For a mortgage, the effective cost depends on points, closing costs, and how long you hold the loan.
A comparison checklist
- Confirm compounding frequency and whether the rate is variable or fixed.
- Include fees/points when comparing loans (APR may not capture everything).
- Use the same time horizon: holding 2 years vs 10 years changes which option wins.
Common mistakes
- Comparing APRs with different compounding conventions.
- Confusing APY (nominal compounding) with real return (inflation-adjusted).
- Ignoring fees and points that change the effective cost/return.
- Using APR as if it were the same as the monthly rate (APR/12 is the monthly nominal rate, not an effective rate).