Interest Rate Converter (Nominal, Effective, Monthly)
Convert any interest rate into its equivalents: nominal annual to effective annual, effective annual to monthly, quarterly or daily, and rates paid in advance — all compounding frequencies in one table.
How it works
Nominal j with m periods: i = j ÷ m · effective annual: i = (1 + EA)^(1/m) − 1 · paid in advance: i = (j ÷ m) ÷ (1 − j ÷ m) · EA = (1 + i)ᵐ − 1 · effective rate for k periods a year = (1 + EA)^(1/k) − 1 · nominal = k × that rate · continuous = ln(1 + EA)
The same cost of money can be written many ways: a nominal annual rate with monthly compounding, an effective annual rate, a monthly effective rate, or a rate charged in advance (common in Colombian and Latin American banking as “tasa anticipada”). Two rates are equivalent when they produce the same amount after one year. The calculator first reduces your rate to an effective rate per period, compounds it to the effective annual rate, and from there rebuilds every other form. Use the effective annual rate to compare offers.
Worked example
A 24% nominal annual rate compounded monthly is 2% a month. Compounded over 12 months that is an effective annual rate of 1.02¹² − 1 = 26.8242%. The same rate is 6.12% a quarter, 0.0650% a day, 23.53% nominal annual paid monthly in advance, and 23.76% compounded continuously.
Sources: Wikipedia — Effective interest rate · Wikipedia — Nominal interest rate
Frequently asked questions
How do I convert an annual rate to a monthly rate?
If it is a nominal annual rate compounded monthly, divide by 12. If it is an effective annual rate, use (1 + EA)^(1/12) − 1 — dividing by 12 would overstate it.
What is a rate paid in advance (anticipated)?
Interest charged at the start of each period instead of the end. Because you pay sooner, the equivalent rate paid in arrears is higher: i = d ÷ (1 − d) per period.
Which rate should I use to compare loans or deposits?
The effective annual rate (also called EAR, APY, TEA or EA). It puts every compounding frequency on the same yearly footing.
Why is the effective rate higher than the nominal?
Because interest earned in early periods also earns interest. The more frequent the compounding, the bigger the gap.
Related calculators
Estimates for education and planning, not financial advice. Lenders’ contracts, fees, day-count and rounding rules differ — check the official cost disclosure (APR / TAE / CAT) in your loan or card agreement before deciding.