How to use the apr to apy calculator
- Choose whether to convert APR to APY or APY to APR.
- Enter the rate as a percent and choose how often interest compounds.
- Optionally enter a deposit to see the interest in one year.
- Read the converted rate, the extra yield from compounding and the table showing the APY at each compounding frequency.
Formula
APY = (1 + APR / n)^n - 1
APR = n x ((1 + APY)^(1/n) - 1)
Continuous compounding: APY = e^APR - 1 and APR = ln(1 + APY)
n = compounding periods per year
APR is the stated annual rate before compounding. APY is the effective yield after compounding for a year.
Worked example
A 5% APR compounded monthly has an APY of (1 + 0.05 / 12)^12 - 1 = 5.1162%. On $10,000, the balance after a year is $10,511.62. Daily compounding gives 5.1267%, and continuous compounding gives 5.1271%.
Going the other way, an APY of 5.12% with monthly compounding is an APR of 12 x (1.0512^(1/12) - 1) = 5.0036%. With annual compounding, APR and APY are the same, so 5% stays 5%.
APR and APY in plain terms
APR is the simple annual rate before the effect of compounding. APY includes it, so it is the true return for a year if you leave the interest in. The more often interest is added, the higher the APY for the same APR, though the difference is small beyond monthly compounding. Savings accounts and CDs usually advertise APY, and loans usually advertise APR.
Comparing offers
Compare savings accounts by APY, since that already includes how often interest compounds. For loans the APR on a disclosure can include fees, which is a different calculation. See the APR calculator for loans with fees, and the CD calculator and the savings calculator for what a balance grows to.
Growth over time
A rate converted to APY can be used to project a balance over several years with the compound interest calculator. Rates on savings accounts can change, so the figure is true only while the rate holds.
Assumptions and limits
- The rate stays the same for the whole year.
- Interest is added at equal intervals, and there are 365 days when you choose daily compounding.
- Fees, taxes and minimum balances are not included.
- Money is rounded to the cent and rates are shown to four decimals.
Frequently asked questions
How do you convert APR to APY?
Add the APR divided by the number of periods to 1, raise it to the number of periods and subtract 1.
Is APY always higher than APR?
Whenever interest compounds more than once a year, yes. With annual compounding they are equal.
How does daily compounding compare with monthly?
Slightly higher. At a 5 percent APR, daily compounding gives 5.1267 percent and monthly gives 5.1162 percent.
Which should I use to compare savings accounts?
The APY, because it already includes compounding, so accounts with different compounding can be compared directly.