What this calculator does
A nominal interest rate quoted per year understates the true cost or return once compounding is taken into account, because interest earned or charged during the year itself starts earning or costing interest before the year is out. The effective annual rate, sometimes called the effective interest rate or annual equivalent rate, restates that nominal figure as the actual percentage return or cost over a full year.
This effective interest rate calculator converts a nominal annual rate compounded a chosen number of times per year into its effective annual rate, and can also run the calculation in reverse: given a target effective rate, it works out the nominal rate needed to achieve it at a given compounding frequency, which is the question behind searches for a nominal interest rate calculator.
The formula
Divide the nominal annual rate by the number of compounding periods per year, add 1, raise that to the power of the number of periods, then subtract 1: EAR = (1 + nominal/n)^n minus 1. The reverse direction solves the same equation for the nominal rate given a target effective rate.
| Term | Meaning |
|---|---|
| Nominal interest rate | The stated annual rate before accounting for the effect of compounding within the year. |
| Effective annual rate (EAR) | The actual annual rate once compounding within the year is folded in, always equal to or greater than the nominal rate for a positive rate. |
| Compounding periods per year | How often interest is calculated and added within the year, such as 12 for monthly or 365 for daily compounding. |
The inputs explained
| Field | What to enter |
|---|---|
| Calculate | Choose whether you know the nominal rate and want the effective rate, or know a target effective rate and want the nominal rate needed. |
| Nominal annual rate (or target effective rate, if reversed) (%) | The nominal annual rate as a percentage, or the target effective annual rate as a percentage if solving in reverse. |
| Compounding periods per year | How many times per year interest compounds: 12 for monthly, 4 for quarterly, 365 for daily, and so on. |
When to use it
How to calculate effective interest rate on a loan or card
A credit product quotes a nominal annual rate with monthly or daily compounding; converting it to the effective annual rate shows the true annual cost of carrying a balance, which is usually higher than the headline rate suggests.
Comparing two rates with different compounding frequencies
A loan compounding monthly and one compounding daily cannot be compared fairly by their nominal rates alone. Converting both to effective annual rates puts them on the same footing.
Working backwards to a target using a nominal interest rate calculator
If a savings goal requires a certain effective annual return, running the calculation in reverse shows what nominal rate, at a given compounding frequency, would actually deliver it.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the effective rate rises with compounding frequency, at a fixed nominal rate
The same 6% nominal rate, compounded at increasingly frequent intervals.
How the effective rate rises with the nominal rate, at monthly compounding
A range of nominal annual rates, each compounded monthly.
Questions
How do you calculate effective interest rate?
Take the nominal annual rate, divide it by the number of compounding periods per year, add 1, raise the result to the power of the number of periods, then subtract 1. The output is the effective annual rate as a decimal or percentage.
Why is the effective rate always higher than the nominal rate?
Because interest earned or charged partway through the year starts compounding on itself before the year ends, adding a little extra beyond the simple nominal figure, for any positive rate and more than one compounding period per year.
What is a nominal interest rate calculator used for?
It runs the effective rate formula in reverse: starting from a target effective annual rate, it solves for the nominal rate, at a chosen compounding frequency, that would produce it.
Does compounding frequency matter much in practice?
It matters more at higher rates and can matter for comparing similar products, but the difference between very frequent compounding options, such as daily versus continuous, is usually small. The bigger gap is typically between annual compounding and anything more frequent.
For working out the discount rate implied by a present and future value instead, see the discount rate calculator.