APR vs APY Calculator
Two Rates That Describe the Same Product Differently
A savings account advertised at "5% APR compounded monthly" and one advertised at "5.12% APY" can be the exact same product, described from two different angles. APR is the nominal annual rate before compounding is applied; APY (annual percentage yield) is the effective rate after compounding is folded in. Lenders tend to advertise the lower-looking APR; savings and investment products tend to advertise the higher-looking APY. This calculator converts cleanly between the two in either direction.
The Formula
APR = n × ((1 + APY)1/n − 1)
n is the number of compounding periods per year — 12 for monthly, 365 for daily, 4 for quarterly, and so on. The more frequently interest compounds, the larger the gap between APR and APY becomes.
Where This Matters
- Comparing savings accounts — two accounts with different compounding frequencies aren't directly comparable by their stated APR alone; converting both to APY puts them on equal footing.
- Reading loan disclosures — APR is the figure required on most loan disclosures, but the true annual cost, if interest compounds within the year, is slightly higher and better represented by APY.
- Credit card math — credit cards typically compound daily, meaning the APY on a carried balance is meaningfully higher than the advertised APR.
Worked Example
| Compounding | Periods per year (n) | Resulting APY |
|---|---|---|
| Monthly | 12 | 5.1162% |
| Daily | 365 | 5.1267% |
More frequent compounding (daily vs. monthly) produces a slightly higher APY from the same 5% APR.
How to Use This Calculator
- Choose the conversion direction: APR to APY, or APY to APR.
- Enter the known rate — APR or APY, as a percentage.
- Enter the number of compounding periods per year (e.g. 12 for monthly).
- Select Calculate to get the converted rate.
Related Calculations
See the Future Value Calculator to project balances using either rate, or the Rule of 72 Calculator for a quick doubling-time estimate from an APY figure.