APR to APY Calculator (Effective Annual Rate)
APR to APY Calculator (Effective Annual Rate)
Turn a quoted annual rate and how often it compounds into the effective annual rate (APY) it really pays or costs — and turn an effective rate back into a nominal one.
Effective annual rate
7% a year compounded quarterly
Effective annual rate
Reverse: r = m × [(1 + EAR)1 ÷ m − 1]; continuous: r = ln(1 + EAR)
- r
- the nominal annual rate, as a decimal
- m
- compounding periods in a year: 1, 2, 4, 12, 52 or 365
- EAR
- the effective annual rate — in the US, the annual percentage yield (APY)
Worked example
7% a year compounded quarterly
Rate per quarter = 7 ÷ 4 = 1.75%
(1.0175)4 = 1.071859
EAR = 1.071859 − 1 = 7.186%
The same yield compounded monthly would be quoted as 6.960%
Effective annual rate by compounding frequency
| Compounding | 7% nominal | 12% nominal |
|---|---|---|
| Yearly | 7.000% | 12.000% |
| Half-yearly | 7.122% | 12.360% |
| Quarterly | 7.186% | 12.551% |
| Monthly | 7.229% | 12.683% |
| Weekly | 7.246% | 12.734% |
| Daily | 7.250% | 12.747% |
| Continuous | 7.251% | 12.750% |
Nominal, effective and APR — three words for different things
A nominal rate is the annual figure a bank quotes. If interest is added more than once a year, each credit starts earning interest itself, so the rate you actually earn over a year is a little higher. That is the effective annual rate: 7% compounded quarterly is 7.186% a year. In the United States it is called the annual percentage yield (APY), and Regulation DD requires banks to show it on deposits, so accounts that compound differently can be compared.
The reverse is useful when two products quote rates on different bases. An effective 8% a year is the same as 7.721% compounded monthly. Enter an effective rate in the reverse box to see the nominal rate at the compounding you chose.
APR is where people go wrong. On a loan, the annual percentage rate is not simply the nominal interest rate. US Regulation Z builds certain fees into it, and the Reserve Bank of India’s Key Facts Statement defines APR as the annual cost of credit including all other charges. Feeding a loan APR into this page treats those fees as if they were interest compounding, which they are not. Use the page for the pure conversion between a nominal rate and its effective rate — for example a credit card’s monthly rate, or a deposit that compounds quarterly.
Two caveats. The effective rate assumes the interest is left in; with a payout deposit it is paid out and does not compound, so you earn only the nominal rate. And it is before tax. For a whole deposit, try the FD calculator or the compound interest calculator; to see how long money takes to double at a given rate, the rule of 72 calculator. This is arithmetic on the figures you enter, not financial advice.
Frequently asked questions
How do you convert APR to APY?
APY = (1 + r ÷ m)m − 1, where r is the nominal annual rate as a decimal and m the compounding periods in a year. 7% compounded quarterly is 7.186%.
Is a loan’s APR the same as its nominal rate?
Not usually. Under US Regulation Z and in India’s Key Facts Statement, a loan’s APR includes certain fees and charges as well as interest. Converting it as if it were a nominal rate gives a misleading figure.
How much difference does daily compounding make?
Little beyond monthly. At 12%, monthly compounding gives 12.683%, daily 12.747% and continuous 12.750%.
How do I convert an effective rate back to a nominal rate?
r = m × [(1 + EAR)1 ÷ m − 1]. An effective 8% equals 7.721% compounded monthly.
Related calculators
References
- Consumer Financial Protection Bureau. Regulation DD (Truth in Savings), 12 CFR Part 1030, Appendix A — Annual Percentage Yield Calculation: APY = 100 [(1 + Interest ÷ Principal)365 ÷ days in term − 1].
- Consumer Financial Protection Bureau. Regulation Z (Truth in Lending), 12 CFR Part 1026, §1026.22: the annual percentage rate of a loan reflects the finance charge, which includes certain fees as well as interest.
- Reserve Bank of India. Key Facts Statement (KFS) for Loans & Advances. Circular, 15 April 2024: the Annual Percentage Rate (APR) is the annual cost of credit, including interest and all other charges.
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance. McGraw-Hill. Compound interest, effective annual rates, continuous compounding and the future value of an annuity.