A rate quoted per year is not the same as the rate you actually pay. When interest compounds monthly, the effective annual rate is higher than the nominal annual rate. This table converts between them.
Monthly rate = nominal annual rate ÷ 12. Effective annual rate = (1 + monthly rate)^12 − 1. For example, a 6% nominal rate compounded monthly is 0.5% per month, and the effective annual rate is (1.005)^12 − 1 = 6.17%.
| Nominal annual rate | Monthly rate | Effective annual rate |
|---|---|---|
| 2.0% | 0.1667% | 2.0184% |
| 2.5% | 0.2083% | 2.5288% |
| 3.0% | 0.2500% | 3.0416% |
| 3.5% | 0.2917% | 3.5567% |
| 4.0% | 0.3333% | 4.0742% |
| 4.5% | 0.3750% | 4.5940% |
| 5.0% | 0.4167% | 5.1162% |
| 5.5% | 0.4583% | 5.6408% |
| 6.0% | 0.5000% | 6.1678% |
| 6.5% | 0.5417% | 6.6972% |
| 7.0% | 0.5833% | 7.2290% |
| 7.5% | 0.6250% | 7.7633% |
| 8.0% | 0.6667% | 8.3000% |
| 8.5% | 0.7083% | 8.8391% |
| 9.0% | 0.7500% | 9.3807% |
| 9.5% | 0.7917% | 9.9248% |
| 10.0% | 0.8333% | 10.4713% |
| 10.5% | 0.8750% | 11.0203% |
| 11.0% | 0.9167% | 11.5719% |
| 11.5% | 0.9583% | 12.1259% |
| 12.0% | 1.0000% | 12.6825% |
APR is the nominal yearly cost of borrowing, usually quoted without compounding. APY (annual percentage yield) is the effective rate after compounding, so it is the number to compare when two offers compound differently. A 6% APR compounded monthly is a 6.17% APY; compounded daily it would be 6.18%.
A credit card quotes 24% APR compounded monthly. The monthly rate is 24% ÷ 12 = 2%, and the effective annual rate is (1.02)^12 − 1 = 26.82%. That is why card interest grows faster than the headline rate suggests.
These tables assume monthly compounding unless stated otherwise. Loans and cards that compound daily, or charge fees, have a higher effective cost than the table shows.