How this calculation works
j is the nominal annual rate as a decimal and m is the number of compounding periods in one year. Interest stays in the account and earns the same periodic rate. The difference between effective and nominal rates is shown in percentage points.
Effective rate = [(1 + j/m)ᵐ − 1] × 100%A worked example
A nominal 12% rate compounded monthly is 1% per month. After 12 periods, its effective annual rate is approximately 12.682503%.
Good to know
A fixed-rate mathematical conversion. Does not calculate legally defined loan APR or certify an APY disclosure. No fees, tax, tiering, irregular days, withdrawals or changing interest rates.
The same annual label can hide different compounding
A nominal 12% rate divided into monthly periods means 1% for each period. Retaining each month’s interest makes the next month’s base a little larger. After a full year, the growth is about 12.6825%, rather than exactly 12%.
Compare the yearly and monthly options using the same nominal rate to isolate the effect of compounding. This comparison assumes the interest stays in place. If you withdraw every interest payment, the balance does not follow the same compound-growth path.
The lift is reported in percentage points. An effective rate of 12.6825% minus a nominal rate of 12% is a 0.6825 percentage-point difference, not an increase of 0.6825% relative to the nominal number.
Compare a product’s actual terms as well as the conversion
A mathematical conversion is only one part of comparing products. Two offers with identical effective rates can differ in fees, withdrawal restrictions, minimum balances, interest crediting and tax treatment. Record those terms separately before deciding whether the offers are comparable.
Do not enter an already-effective annual rate and compound it again as if it were nominal. If a rate includes the year’s compounding, using it as the nominal input double counts that effect.
The daily option means 365 equal periods in a one-year model. It does not implement a bank’s leap-year treatment, daily balance method or disclosure rules. Similarly, the tool is not a statutory APR calculator for borrowing costs.
A few questions, answered
Why does annual compounding return the nominal rate?
There is only one compounding period in the year, so there is no extra within-year interest on interest.
Will more frequent compounding always make a large difference?
No. The size of the difference depends on the nominal rate. At zero rate, every frequency gives zero; at modest positive rates, the lift may be small.
Can I convert a monthly rate directly?
The input is nominal annual rate. A periodic rate of 1% per month corresponds to nominal annual 12% in this model.