Effective annual rate calculator — the real yearly rate after compounding

How to use the effective annual rate calculator

1. Enter the Nominal annual rate as quoted, for example 7.
2. Choose the Compounding: Yearly, Half-yearly, Quarterly, Monthly, Daily or Continuous.
3. Read Effective annual rate (APY), the Nominal rate and the Difference, then compare all six frequencies in the table.

What it does and when to use it

Two offers can quote the same rate and still pay different amounts, because one compounds more often. A fixed deposit at 7% compounded quarterly beats a bond paying 7% once a year. Turning each quote into an effective annual rate puts them on equal terms.

The same check works for borrowing. A lender quoting 1.5% a month is charging 18% nominal, and more than that once the monthly compounding is counted. Enter 18 with monthly compounding to see it.

To see what the effective rate does to a real amount over several years, use the future value calculator. For a deposit with its own quarterly compounding, the FD calculator shows the maturity value. The APY calculator gives a deposit-focused version of the same yield. If you are comparing pay rather than interest, the hourly to annual salary calculator converts wages instead.

How it works

For k compounding periods a year and a nominal rate i (as a decimal):

EAR = (1 + i ÷ k)^k − 1

For continuous compounding:

EAR = e^i − 1

The Difference is EAR minus the nominal rate, which is how much compounding adds over a year. The table repeats the formula for all six frequencies at your nominal rate. The CFPB’s Regulation DD appendix uses the same compounding idea to define APY, raising one period’s growth to the power that fills a 365-day year.

Worked examples

These figures come from the calculator’s own function.

12% compounded monthly. Effective annual rate 12.683%, a difference of 0.683%. The table shows 12% yearly, 12.36% half-yearly, 12.551% quarterly, 12.683% monthly, 12.747% daily and 12.75% continuous.

7% compounded quarterly, a common bank deposit convention in India. Effective annual rate 7.186%. Monthly compounding at the same 7% would give 7.229%.

10% compounded continuously. Effective annual rate 10.517%, difference 0.517%.

Limits and tips

• Fees are not included. For a loan, an effective rate that includes charges will be higher still.
• Fixed rate assumed for the whole year.
• Use the frequency the product really uses. Check the terms; some accounts compound daily but credit interest monthly.
• The calculation runs in your browser.