Interest basics Updated November 2026

Effective annual rate

The effective annual rate is the yearly rate that gives the same result as a nominal rate compounded m times a year: EAR = (1 + i/m)^m - 1. It lets you compare rates with different compounding frequencies on equal terms. With continuous compounding, EAR = e^i - 1.

Syntax

EAR = (1 + i/m)^m - 1   (continuous: EAR = e^i - 1)

Part	What it is
`i`	Nominal (stated) annual rate as a decimal
`m`	Number of compounding periods per year

Examples

8% compounded semiannually
EAR = (1 + 0.08/2)^2 - 1

Result: EAR = 8.16%

Excel: =EFFECT(8%, 2)

10% compounded monthly
EAR = (1 + 0.10/12)^12 - 1

Result: EAR = 10.47%

Excel: =EFFECT(10%, 12)

5% compounded continuously
EAR = e^0.05 - 1

Result: EAR = 5.13%

Excel: =EXP(5%)-1

Common mistakes

Comparing a 7.9% monthly-compounded loan to an 8% yearly-compounded one by the stated rates: the monthly one costs 8.19% effective, so it is more expensive.
Raising to the power m but forgetting to divide i by m first.
Using EAR as the periodic rate in a monthly payment formula; the payment formula needs the rate per period (i/m), not the effective annual rate.

Practice Effective annual rate

These drills check your answer on live data, free, no account needed.

Effective rate from a monthly APRA store credit card charges 6.25% APR, compounded monthly. What is the effective annual rate?
Effective rate with daily compoundingA short-term business line of credit charges 8.25% APR, compounded daily on a 365-day year. What is the effective annual rate?
Continuous compoundingA fund grows at 2.25% per year, compounded continuously. What does a $1,000 investment grow to in 15 years?

Questions

What is the difference between nominal and effective interest rate?

The nominal rate is the stated yearly rate ignoring compounding within the year. The effective rate includes compounding, so it is what you actually earn or pay. They are equal only with yearly compounding.

How do I find the effective monthly rate from an EAR?

monthly rate = (1 + EAR)^(1/12) - 1. For EAR 6% the monthly rate is 0.487%, not 0.5%.

APR vs APYAPR is the yearly rate without compounding; APY includes it. Convert with APY = (1 + APR/n)^n - 1, worked examples and the Excel EFFECT and NOMINAL functions.
Continuous compoundingContinuous compounding uses A = P x e^(rt), the limit of compounding infinitely often. Examples, the effective rate e^r - 1, doubling time and Excel EXP.
Compound interestThe compound interest formula A = P(1 + r/n)^(nt), what each symbol means, examples for yearly and monthly compounding, the Excel FV function and errors.
Mortgage payment formulaHow to calculate a monthly mortgage payment with M = P x r / (1 - (1 + r)^-n). Examples for 200,000 at 6% and 300,000 at 5%, Excel PMT and common mistakes.