Effective rates tell you what money really grows by in a year, but many calculations — loan payments, periodic interest, spreadsheet formulas — need the nominal rate that sits behind them. This calculator reverses the compounding: give it an effective annual rate or APY and a compounding frequency, and it returns the nominal annual rate and the rate applied each period.
How to use the nominal interest rate calculator
- Enter the effective annual rate — the APY on a savings account, or an annualized return.
- Choose the compounding frequency you want the nominal rate expressed in.
- Read the nominal rate and the rate per period, then compare all frequencies and common APYs in the tables.
Nominal rate formulas
EAR is the effective annual rate as a decimal and m is the number of compounding periods per year. The bracketed part, (1 + EAR)1/m − 1, is the rate per period.
Worked example
A bank advertises a 5% APY and compounds monthly. What nominal rate is it paying?
Rate per month: 1.051/12 − 1 = 0.00407412, or 0.407412%
Nominal annual rate: 12 × 0.00407412 = 4.8889%
Check: (1 + 0.048889 ÷ 12)12 − 1 = 5.0000%
Nominal rates that give a 5% effective yield
| Compounding | Nominal rate | Rate per period |
|---|---|---|
| Annually | 5.0000% | 5.000000% |
| Semi-annually | 4.9390% | 2.469508% |
| Quarterly | 4.9089% | 1.227223% |
| Monthly | 4.8889% | 0.407412% |
| Daily | 4.8793% | 0.013368% |
| Continuously | 4.8790% | — |
The differences are small at low rates and grow at higher ones: a 12% effective rate is 11.3866% nominal with monthly compounding.
When you need the nominal rate
Building a payment or growth schedule
Loan and annuity formulas use the rate per period. If you start from an effective rate, convert it here first and divide by the number of periods.
Matching a savings goal to an account
If a target return is stated as an effective rate, the nominal rate tells you what an account compounding monthly or daily would need to advertise.
Reading disclosures
US loans disclose APR, a nominal rate, while deposit accounts disclose APY, an effective rate. Converting between them lets you compare a loan’s cost with a savings yield on the same basis.
To go the other way, from nominal to effective, use the effective annual rate calculator. To restate a nominal rate under a different compounding frequency directly, use the equivalent interest rate calculator.
These are exact mathematical conversions. Rates offered by banks and lenders may be rounded, and disclosures follow their own regulatory rules.
Frequently asked questions
What is a nominal interest rate?
A nominal rate is the annual rate stated before compounding — the rate per period multiplied by the number of periods in a year. It is the form used for APRs and for most quoted loan and savings rates. The effective rate is what you actually earn or pay once compounding is included.
How do I convert APY to a nominal rate?
Use r = m × [(1 + APY)^(1/m) − 1], where m is the number of compounding periods per year. A 5% APY compounded monthly corresponds to a nominal rate of 12 × (1.05^(1/12) − 1) = 4.8889%.
What about continuous compounding?
For continuous compounding, the nominal rate is the natural logarithm of one plus the effective rate: r = ln(1 + APY). A 5% effective rate equals 4.879% compounded continuously.
Why is the nominal rate lower than the APY?
Compounding adds interest on interest, so a smaller stated rate is enough to reach the same effective yield. The more often interest compounds, the lower the nominal rate needed.