How to use this calculator
- Convert: choose APR → APY to find the yield from a stated rate, or APY → APR to find the stated rate behind an advertised APY.
- Rate and Compounding: enter the rate and how often interest is added. Many savings accounts compound daily and credit monthly. CDs vary, so check the account disclosure.
- Balance and Period: optional. Enter a balance and a number of months to see the interest you’d earn, assuming no deposits or withdrawals.
The table under the result compares every compounding frequency at the same rate, so you can see how much the frequency matters.
The APY formula
- r is the stated annual rate as a decimal (4.5% = 0.045)
- n is the number of compounding periods per year (12 for monthly, 365 for daily)
For continuous compounding the formula becomes APY = e^r − 1. Going the other way, the stated rate for a given APY is:
Interest over any period follows from the APY: a balance B earns B × ((1 + APY)^(months/12) − 1).
Worked example
A high-yield savings account pays 4.5% compounded daily.
- Daily rate: 4.5% ÷ 365 = 0.01233%.
- One year of growth: (1 + 0.0001233)^365 = 1.046025.
- Subtract 1: APY = 4.602%.
On $10,000 that’s $460.25 of interest in a year, $10.25 more than the stated 4.5% suggests. Over 24 months the same account earns about $941.68, because the second year’s interest is earned on a larger balance.
Working backward, an account advertising a 5% APY with monthly compounding has a stated rate of 4.889%. With daily compounding the stated rate would be 4.879%.
APY by compounding frequency
The same 5% stated rate, compounded at different frequencies:
| Compounding | APY | Interest on $10,000 in a year |
|---|---|---|
| Annually | 5% | $500.00 |
| Semiannually | 5.062% | $506.25 |
| Quarterly | 5.095% | $509.45 |
| Monthly | 5.116% | $511.62 |
| Daily (365) | 5.127% | $512.67 |
| Continuously | 5.127% | $512.71 |
Going from annual to monthly compounding adds about $12 a year on $10,000. Going from monthly to daily adds about $1.
APR to APY conversion table
| Stated rate | Quarterly | Monthly | Daily |
|---|---|---|---|
| 1% | 1.004% | 1.005% | 1.005% |
| 2% | 2.015% | 2.018% | 2.020% |
| 3% | 3.034% | 3.042% | 3.045% |
| 4% | 4.060% | 4.074% | 4.081% |
| 5% | 5.095% | 5.116% | 5.127% |
| 6% | 6.136% | 6.168% | 6.183% |
| 8% | 8.243% | 8.300% | 8.328% |
| 10% | 10.381% | 10.471% | 10.516% |
The gap between rate and yield widens as rates rise. At 1% it’s barely visible, while at 10% daily compounding adds more than half a percentage point.
The same math on debt
Compounding works against you on a loan. A credit card with a 24% APR that compounds monthly has an effective annual rate of 26.824%, and with daily compounding it’s 27.115%. For loans, though, the APR you’re quoted under the Truth in Lending Act can also include some fees, so it isn’t always just the interest rate. Our APR calculator works out a loan’s true APR with fees.
Tips for comparing rates
- Compare APY to APY. It’s the one number that puts accounts with different compounding on equal terms.
- Watch for teaser rates and tiers. A high APY may apply only for a few months or only up to a certain balance.
- Count inflation. A 4.5% APY with 3% inflation grows your buying power by only about 1.5% a year. The inflation calculator shows the effect over time.
- Taxes matter too. Interest on savings and CDs is taxed as ordinary income each year, even if you leave it in the account.
To project growth with regular deposits, use the compound interest calculator or the savings calculator.
Assumptions and limitations
Daily compounding uses a 365-day year. Some institutions use 360 days or 366 in a leap year, which changes the yield slightly. Interest for periods other than whole years is figured from the APY, so it can differ by a few cents from a bank’s day-count method. Results assume the rate stays the same and no money is added or taken out.
Sources
- Regulation DD (Truth in Savings), Appendix A to Part 1030: Annual Percentage Yield Calculation
- CFPB: Regulation DD, Truth in Savings
- CFPB: Regulation Z, Truth in Lending
Results are estimates for comparison. Check your account disclosure for the exact APY and compounding method.
Frequently asked questions
What is the difference between APR and APY?
APR, or the stated interest rate, is the simple yearly rate before compounding. APY includes the effect of earning interest on your interest during the year. A 4.5% rate compounded daily works out to a 4.602% APY, so the APY is always equal to or higher than the rate when interest compounds more than once a year.
How do you calculate APY?
Divide the annual rate by the number of compounding periods, add 1, raise the result to the number of periods, and subtract 1. For 5% compounded monthly, that's (1 + 0.05/12)^12 − 1 = 5.116%. For continuous compounding, APY = e^r − 1.
Does daily compounding make a big difference?
Not much compared with monthly. At 5%, monthly compounding gives a 5.116% APY and daily compounding gives 5.127%, a difference of about $1 a year on $10,000. The rate itself matters far more than how often it compounds.
Should I compare savings accounts by APR or APY?
By APY. US banks must disclose the APY on deposit accounts under the Truth in Savings Act, and it already reflects compounding, so it lets you compare accounts that compound differently on equal terms. Use the interest rate only when you need to know the per-period rate.
How much interest will $10,000 earn in a year?
At a 4.5% interest rate compounded daily, about $460.25 in a year, which matches its 4.602% APY. At a 4.5% APY it's exactly $450, whatever the compounding. The calculator shows the interest for any balance and period.
Is APY the same as the effective annual rate?
Yes, they're the same idea. APY is the term used for deposit accounts in the US, while effective annual rate (EAR) is the general finance term. Both measure one year of growth including compounding.
Updated November 2026. Results are estimates for educational purposes and depend on the inputs you provide.