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EAR Calculator

Convert a nominal rate into the effective annual rate, and compare every compounding frequency at once.

Inputs
EAR resultCalculated
Effective annual rate12.68250%
Formula
EAR(1 + r / n) ^ n - 1
With continuous compounding, EARe ^ r - 1
Inputs
  r   nominal annual rate   12.00%
  n   compounding           12 (monthly)
Working
r / n0.12 / 12 = 0.01
(1 + 0.01) ^ 121.1268250301
EAR1.1268250301 - 1 = 0.12682503
Results
  Effective annual rate                12.68250%
  Nominal rate                         12.00000%
  Extra from compounding               0.68250%
  Cost on 10,000 borrowed for a year   1,268.25
Same nominal rate at other frequencies
once a year12.00000%
twice a year12.36000%
quarterly12.55088%
monthly12.68250%
weekly12.73410%
daily12.74746%
continuously12.74969%
Runs locally in your browser

About the EAR Calculator

The effective annual rate is what a quoted rate actually costs or earns over a year once interest starts earning interest. A credit card advertising 12 percent compounded monthly really charges 12.6825 percent, and the gap widens as the rate rises: at 24 percent nominal the effective figure passes 26.8 percent. Borrowers meet this most often on cards and short term loans, where monthly or daily compounding is standard.

Every result includes a comparison block running the same nominal rate through annual, half yearly, quarterly, monthly, weekly, daily and continuous compounding. Reading down that list shows how quickly the benefit flattens. Going from annual to monthly on a 12 percent rate adds 0.68 percentage points; going from daily to continuous adds barely two thousandths. Continuous compounding, computed as e raised to the rate minus one, is the mathematical ceiling that all the others approach.

The cash line puts the abstraction into money by showing what a year of interest costs on 10,000 borrowed. Use the effective rate whenever two offers quote different compounding schedules, because comparing nominal rates in that situation is meaningless. Savers looking at the same idea from the other side will find the APY Calculator framed in deposit language, and the Car Loan Calculator turns an APR into an actual monthly payment.

How to use

  1. Enter the nominal annual rate exactly as quoted.
  2. Choose the compounding frequency, or pick Continuously for the theoretical maximum.
  3. Read the effective annual rate and the extra it adds over the nominal figure.
  4. Scan the comparison block to see the same rate under every other schedule.

Common questions

What is the effective annual rate formula?
EAR = (1 + r / n) ^ n - 1, where r is the nominal rate and n is the compounding periods per year. With continuous compounding it becomes e raised to r, minus one.
Is EAR the same as APY?
The maths is identical. APY is the term used for deposits and savings, while EAR is normally used when discussing the cost of borrowing.
What does continuous compounding mean?
Interest is credited over infinitely small intervals. It sets the upper limit for any nominal rate and is used widely in options pricing formulas.
Why does my card statement show a bigger number?
Card APRs often exclude fees that a regulated total cost figure must include, and some issuers compound daily. Check the compounding basis before comparing.