Join the waitlist

Effective Annual Rate CalculatorAPR to EAR by Compounding

What is this money worth, or what does it cost, over time?

Effective annual rate from a nominal APR compounded annually through daily or continuously, with the periodic rate and a year of interest.

  • Runs in your browser
  • Nothing stored or sent
  • Free, no sign-up
Your figures
Example figuresIllustrative only. Type over them with your own.
Effective annual rate
28.38%
Rate actually earned or paid over a year with compounding
Periodic rate
0.07%
Interest on the balance over one year
$1,419
Drawn to one scale
Effective annual rate28.38%
Periodic rate0.07%
Gap between EAR and APR3.39%
All results
MeasureResult
Effective annual rate28.38%
Periodic rate0.07%
Interest on the balance over one year$1,419
Gap between EAR and APR3.39%
How this was worked out
Work shownrecomputed as you type
EAR = (1 + APR / m)^m - 1
Continuous: EAR = e^APR - 1
Periodic rate = APR / m

Illustrative arithmetic on the figures you enter. Check the result against your firm's methodology before relying on it.

The formulas

  • EAR = (1 + APR / m)^m - 1
  • Continuous: EAR = e^APR - 1
  • Periodic rate = APR / m

How it works

The APR quoted on a loan or card is a nominal rate: the periodic rate times the number of periods. When interest compounds, each period charges interest on earlier interest, so the effective annual rate is higher. The gap widens with the rate and the compounding frequency.

Credit cards that compound daily charge APR / 365 each day on the balance. A 24.99 percent APR becomes 28.38 percent a year on a balance left unpaid all year. Use EAR to compare offers with different compounding.

Illustrative figures only. Check the result against your firm's methodology before relying on it.

Common questions

Is APY the same as EAR?

Yes. Deposit accounts quote APY, which is the effective annual rate.

Why does my card statement show a daily rate?

Card issuers apply APR / 365 or APR / 360 to the daily balance. Check your agreement.

Does continuous compounding matter in practice?

It is the upper limit. Daily compounding is within a few basis points of it.

Formulas on this page are the standard definitions.

Runs in your browser. The figures you type are not sent to CORAA or stored. Check the result against your firm's methodology before relying on it.

Related audit calculators

CalculatorCPI Inflation Calculator from Two Index ValuesDollar amount restated with the ratio of two CPI index values, the percent change, purchasing power and annualized inflation, per the BLS method.CalculatorReal Interest Rate Calculator (Fisher Equation)Exact real rate from a nominal rate and inflation, the shortcut approximation and the after-tax real rate.CalculatorRule of 72 Calculator with Exact Doubling TimeDoubling time by the rules of 72, 70 and 69.3 against the exact logarithmic answer, with the error of each.
For US CPA firms

Join the CORAA waitlist

CORAA AI drafts audit working papers from your client’s QuickBooks books and does the first pass: lead schedules, tie-out, memos, draft notes and letters. CORAA Network reviewers clear every finding. Your firm reviews and signs.

  • First audit free, so you can judge the quality on a real file
  • Flat fee by entity size; messy books included
  • We work only with CPA firms, never their clients
See how it works →

* required