Interest Rate Conversion Calculator
Turn a rate quoted for one period into the equivalent for any other — monthly, annual, nominal, effective or continuous.
Results
What this tool does
Rates are quoted in incompatible ways, which is what makes offers hard to compare. A credit card says 1.9 per cent a month. A loan says 22 per cent nominal. A deposit says 20.5 per cent effective. Those can be the same rate or very different ones, and there is no telling by eye. Put in whichever figure you have, say what it already is, and this page gives you every other form of the same rate — including the continuous one that financial models use — so you are comparing like with like.
Formula
effective = (1 + nominal ÷ n)^n − 1 · inverse path: nominal = n × ((1 + effective)^(1÷n) − 1)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
rate | The rate | % |
basis | What that rate already is | — |
freq | Payments per year | — |
EA | Effective annual rate | % |
NA | Nominal annual rate | % |
PR | Rate for one period | % |
GP | What compounding adds | % |
MM | Equivalent monthly rate | % |
QQ | Equivalent quarterly rate | % |
HH | Equivalent half-year rate | % |
DD | Equivalent daily rate | % |
CC | Equivalent continuous rate | % |
TE | Growth over ten years | % |
Worked example
- The rate12 %
- What that rate already isnominal
- Payments per year12
- Effective annual rate12.682503 %
- Nominal annual rate12.000000 %
- Rate for one period1.000000 %
- What compounding adds0.682503 %
- Equivalent monthly rate1.000000 %
- Equivalent quarterly rate3.030100 %
- Equivalent half-year rate6.152015 %
- Equivalent daily rate0.032719 %
- Equivalent continuous rate11.940397 %
- Growth over ten years230.0387 %
Limitations
- This is an informational calculator, not personalised financial advice. Rates, fees, taxes and contract conditions vary between institutions and countries.
Frequently asked questions
Why is one per cent a month not twelve per cent a year?
Because in the second month the interest is charged on the first month's interest too. One per cent twelve times over gives 12.68 per cent, not 12. The gap looks small here and grows fast: at two per cent a month it is 26.8 against 24, and at five per cent a month it is 79.6 against 60. This is precisely why lenders must quote an effective annual figure — a nominal rate says nothing until you also know how often it is compounded.
What is the continuous rate for?
It is the rate you would need if interest were added not monthly or daily but at every instant. It is the limit the others approach, and it is always the lowest of them, because compounding more often needs a smaller stated rate to reach the same result. Nobody quotes it to customers, but it is what option pricing and most financial models run on, because it turns multiplying into adding and makes the algebra tractable. If you are feeding a rate into a Black-Scholes formula, this is the one it wants.