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Effective Annual Rate Calculator

Find the true yearly rate after compounding.

Result

19.56%
19.72%

How it is calculated

Enter the nominal annual rate as a percentage and the number of times per year interest is compounded (12 for monthly, 365 for daily, 4 for quarterly, 1 for yearly). With r = nominal ÷ 100 and n compounding periods, the tool computes EAR = (1 + r/n)n − 1. It also shows the limit of continuous compounding, er − 1, as a second figure.

The number of periods must be greater than zero; it does not have to be a whole number. The rate may be zero or negative. Results are percentages with two decimals. Fees and taxes are not included, and what a lender calls APR can include fees in some countries but not others.

Worked example

A card quotes 18% nominal, compounded monthly (n = 12). The monthly rate is 18 ÷ 12 = 1.5%, or 0.015. Over a year, 1.01512 ≈ 1.1956, so the effective annual rate is 19.56%. Compounding continuously instead would give e0.18 − 1 = 19.72%. The gap of about 1.56 points between 18% and 19.56% is the extra cost of monthly compounding.

Try this example →

Common mistakes

  • Typing the monthly rate as the nominal rate. Enter the annual rate (18) and set periods to 12, not 1.5 with 12.
  • Entering the rate as a decimal such as 0.18; the field expects a percentage, so 0.18 means 0.18%.
  • Using the number of years in the periods box. It means compounding events per year.
  • Comparing a nominal rate on one product with an effective rate on another. Convert both to EAR first.
  • Expecting the result to include fees. Only the interest rate and compounding frequency are used.

About this calculator

This calculator converts a nominal annual rate (APR) into the effective annual rate (EAR) that accounts for compounding: EAR = (1 + i/n)^n − 1, where i is the nominal rate and n is the number of compounding periods per year (monthly, daily, etc.). The more frequently interest compounds, the higher the effective rate climbs above the nominal one.

Borrowers and savers use it to compare loan offers, credit cards, or savings accounts that quote the same nominal rate but compound at different frequencies, since the effective rate is what actually accrues over a year. Enter the nominal rate and compounding frequency to see the true annual cost or return.

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