APY calculator
Enter an interest rate and how often it compounds to see the annual percentage yield, the number banks use to compare savings accounts and CDs. Or work backward from an APY to the rate, and see what it earns on your balance.
The yearly rate before compounding, sometimes called APR.
See what it earns in a year at this APY.
The formula
APY = (1 + r ÷ n)n − 1
(1 + 0.04 ÷ 365)365 − 1 = 0.040808 = 4.0808%
r is the rate as a decimal and n is the number of compounding periods a year (365 for daily compounding).
- Interest rate
- 4%
- Compounded
- 365 times a year
- APY, rounded as banks show it
- 4.08%
- APY, exact
- 4.0808%
- APY minus rate
- 0.0808 percentage points
4% at each compounding
| Compounded | APY |
|---|---|
| Daily | 4.0808% |
| Monthly | 4.0742% |
| Quarterly | 4.0604% |
| Semiannually | 4.04% |
| Annually | 4% |
| Continuously | 4.0811% |
- Nothing is uploaded
- Free, no sign-up
- Works on phone and desktop
How to calculate APY
- 1
Choose Rate to APY to turn an interest rate into a yield, or APY to rate to work backward.
- 2
Enter the rate or APY and pick how often interest is compounded: daily, monthly, quarterly, semiannually, annually or continuously.
- 3
Read the APY or rate, rounded the way banks show it and to four decimals, with the formula worked out underneath.
- 4
Add a balance to see the interest it would earn in a year, and compare every compounding in the table.
Features
Both directions
Rate to APY for comparing accounts, or APY back to the rate when you need the number behind an ad.
Six compoundings
Daily, monthly, quarterly, semiannual, annual and continuous compounding, side by side in one table.
Formula shown
The formula with your numbers plugged in, so you can check the result or reuse it in a spreadsheet.
Interest in a year
Add a balance to see what the APY earns in a year, in total and as an average per month.
What APY means
The Truth in Savings Act and its Regulation DD (12 CFR 1030) define the annual percentage yield as a percentage that reflects the total interest paid on an account, based on the interest rate and how often it compounds over a 365-day period. Banks may use a 366-day year in a leap year. An advertisement that states a rate of return on a deposit account has to give it as an annual percentage yield, and the APY is rounded to the nearest hundredth of a percentage point, so 4.0742% appears as 4.07%.
The interest rate is the yearly rate before compounding. When interest is added to the balance more often than once a year, later interest is paid on earlier interest, and the yield ends up higher than the rate. APY folds that into one number, which is why it's the fair way to compare a savings account that compounds daily with a CD that compounds monthly.
The formulas
- APY = (1 + r ÷ n)n − 1, where r is the rate as a decimal and n the compounding periods a year
- Continuous compounding: APY = er − 1
- Rate from an APY = n × ((1 + APY)1/n − 1)
A 4% rate compounded monthly is (1 + 0.04 ÷ 12)12 − 1 = 4.0742%. At 5% compounded daily (365 times) the APY is 5.1267%, and continuous compounding, the upper limit, gives 5.1271%. Working backward, a 4.5% APY needs a rate of 4.402% with daily compounding, or 4.4098% with monthly compounding.
APY for common rates
| Rate | Quarterly | Monthly | Daily |
|---|---|---|---|
| 1% | 1.004% | 1.005% | 1.005% |
| 2% | 2.015% | 2.018% | 2.02% |
| 3% | 3.034% | 3.042% | 3.045% |
| 4% | 4.06% | 4.074% | 4.081% |
| 5% | 5.095% | 5.116% | 5.127% |
| 6% | 6.136% | 6.168% | 6.183% |
Annual compounding always gives an APY equal to the rate, so it isn't shown. The more often interest compounds, the bigger the gap, but at savings rates it stays small.
APY vs APR
APR, the annual percentage rate, is the term for loans and credit cards. Under the Truth in Lending Act it expresses the yearly cost of credit, and it doesn't include compounding. That's why borrowing costs can be higher than the APR suggests: a card balance at a 24% APR that compounds daily and is never paid down grows by about 27.1% in a year. For savings the law asks for APY, which already includes compounding, so the number you see is close to what you earn. When someone quotes a savings "APR", treat it as the interest rate and convert it here.
Using APY to compare accounts
Multiply a balance by the APY to estimate a year's interest: $10,000 at 4.5% APY earns about $450. That assumes the rate stays the same and you leave the interest in. Rates on most savings and money market accounts are variable and can change, while a CD usually fixes its rate for the term but charges a penalty if you take the money out early. Account terms also list minimum balances, fees and how often interest is credited, which can matter as much as a small difference in APY.
To see what a fixed-rate CD earns over its whole term, use the CD calculator. To total up everything you own and owe, try the net worth calculator, and for any other investment the ROI calculator gives the return as a percentage. This page explains how the numbers work; it isn't financial advice.
Frequently asked questions
What is APY?
APY, or annual percentage yield, is the total interest an account pays in a year as a percentage of the balance, including the effect of compounding. US banks and credit unions use it so savers can compare accounts that compound differently.
How do I calculate APY from an interest rate?
Divide the rate by the number of compounding periods a year, add 1, raise it to the number of periods, then subtract 1. For 4% compounded monthly: (1 + 0.04 ÷ 12)^12 − 1 = 4.0742%, which a bank would show as 4.07% APY.
What is the difference between APY and APR?
APR is a yearly rate without compounding, used mainly for loans and credit cards, where it also reflects certain fees. APY includes compounding and is used for savings. With interest compounding more than once a year, the APY is always a little higher than the rate.
How much will $10,000 earn at 4.5% APY?
About $450 in a year, if the rate stays the same and the interest stays in the account. That's the point of APY: the balance times the APY gives a year's interest, whatever the compounding.
Does daily compounding make a big difference?
Not much at savings rates. At 4%, daily compounding gives 4.0808% and monthly 4.0742%, about $0.67 a year apart on $10,000. The rate itself matters far more than how often it compounds.
Can the APY on my savings account change?
Yes, on a variable-rate account the bank can change the rate, and the APY with it. The APY assumes today's rate holds for a whole year. A CD usually locks in its rate for the term.
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