Effective Annual Rate Calculator
Convert a nominal rate (APR) into the effective annual rate (EAR / APY), work back from an effective rate to the nominal rate, or convert a rate between compounding frequencies, from continuous to annual. Includes worked steps, a frequency table, interest on your amount and a side-by-side offer comparison.
How it works
EAR = (1 + r ÷ n)^n − 1 · Continuous: EAR = e^r − 1 · Back to nominal: r = n × ((1 + EAR)^(1 ÷ n) − 1), or ln(1 + EAR) for continuous · Rate per period = r ÷ n
A nominal rate quoted "per year, compounded monthly" is not what you actually earn or pay: the interest credited each period starts earning interest itself. The effective annual rate (EAR, called APY on US savings accounts) turns that into one yearly figure. Here r is the nominal rate as a decimal and n is the number of compounding periods per year. With continuous compounding the formula becomes e^r − 1. The calculator also works backwards: give it an effective rate and it finds the nominal rate that produces it at any frequency, which is how you convert, say, a quarterly-compounded rate into its monthly equivalent. The frequency table shows the same rate under every common schedule, the projection turns the rate into money on your balance, and the comparison tells you which of two offers has the higher effective rate.
Worked example
A 6% nominal rate compounded monthly: EAR = (1 + 0.06 ÷ 12)^12 − 1 = 1.005^12 − 1 = 0.061678, or 6.1678%. On $10,000 that is $616.78 of interest in the first year, $16.78 more than simple interest. Working backwards, an effective 6.1678% with monthly compounding gives 12 × (1.061678^(1/12) − 1) = 6.0000% nominal. Converting 7.24% compounded quarterly to weekly compounding gives about 7.18%, because both have an effective rate of about 7.439%. And comparing 6% monthly with 5.9% daily, the 6% offer wins: 6.1678% against 6.0770% effective.
Sources: Effective interest rate — Wikipedia · Truth in Savings (Regulation DD), Appendix A — APY formula — CFPB
Frequently asked questions
Is EAR the same as APY?
Yes. Banks call it APY (annual percentage yield) on savings; finance textbooks call it the effective annual rate. Both answer the same question: what you actually earn or pay in a year once compounding is included.
Why does compounding frequency matter?
More frequent compounding credits interest sooner, so it starts earning its own interest sooner. Daily beats monthly beats annual, but the effect shrinks quickly: at 6%, monthly gives 6.168%, daily 6.183% and continuous 6.184%.
How do I convert an effective rate back to a nominal rate?
Use Effective → nominal: nominal = n × ((1 + EAR)^(1 ÷ n) − 1). For example, an EAR of 6.1678% with monthly compounding is a 6% nominal rate. For continuous compounding it is ln(1 + EAR).
How do I compare two offers that compound differently?
Turn on Compare with a second offer and enter both rates. Only the effective rates can be compared fairly. A 6% rate compounded monthly (6.168%) beats 5.9% compounded daily (6.077%), even though the daily one compounds more often.
What does Daily (360/yr) mean?
Some lenders and money-market products compound over a 360-day year. With the same nominal rate, 360 compounding periods give a slightly lower effective rate than 365. A loan that charges the daily rate r ÷ 360 for 365 days costs more; check your agreement for the day-count basis.
Is APR the same as the nominal rate?
Usually, for comparing compounding. A US loan APR is a nominal yearly rate that may also include some fees, but it does not include compounding. The EAR shows the yearly cost once interest compounds.
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This is an educational estimate, not financial advice. Lenders use their own rounding, fees and terms — confirm exact figures with your lender or a licensed advisor.