๐ Effective Annual Rate (EAR) Calculator
The more frequently interest compounds, the higher the effective rate is compared to the nominal rate.
Enter a nominal annual interest rate (the stated rate) and how often it compounds per year (monthly, quarterly, daily, etc.) to calculate the Effective Annual Rate (EAR, also called APY) โ the actual annual return you earn or pay. The more frequently interest compounds, the higher the effective rate is compared to the nominal rate.
How to use
- Enter the nominal annual rate (%).
- Enter the number of compounding periods per year, or pick a preset.
- The effective annual rate is calculated automatically.
How the calculation works
The effective annual rate (EAR) is how much money actually grows in a year once you account for how often interest is compounded. EAR = (1 + nominal annual rate รท n)^n โ 1 n is the number of compounding periods per year: 1 for annual, 2 for semi-annual, 4 for quarterly, 12 for monthly and 365 for daily. For the same nominal rate, more frequent compounding means interest earns interest more often, so the EAR is higher. When comparing financial products, compare effective annual rates, which put different compounding frequencies on the same footing, rather than the quoted nominal rates.
Worked example
Nominal rate 12% Annual compounding: 12.000% Quarterly (n = 4): 12.551% Monthly (n = 12): (1 + 0.12 รท 12)^12 โ 1 โ 12.683% Daily (n = 365): 12.747% A 15% nominal rate compounded monthly gives an EAR of about 16.075%.
Things to be aware of
- With continuous compounding (infinitely many periods), the EAR is e^r โ 1 โ about 12.750% for 12% nominal. Daily compounding comes very close.
- Most Japanese bank deposits compound semi-annually (n = 2).
- The APR that Japanese lenders must disclose includes fees and may be defined differently from this calculation.
FAQ
What's the difference between the nominal rate and EAR?
The nominal rate is the stated annual rate as-is. When interest compounds more than once a year, the actual annual return you earn (or pay) ends up higher than the nominal rate โ that actual figure is the Effective Annual Rate (EAR).
What formula is used?
EAR = (1 + nominal rate รท compounding periods)^compounding periods โ 1. When compounding periods = 1 (once a year), EAR equals the nominal rate.
Why does more frequent compounding increase EAR?
The shorter the compounding interval, the more often earned interest gets added to the principal and starts earning interest itself, so the same nominal rate produces a higher effective annual return.