APY Calculator: Convert an Interest Rate to APY and Back
Convert a nominal interest rate into the annual percentage yield (APY) for daily, monthly, quarterly or annual compounding, or find the rate behind an advertised APY, and see the interest a deposit earns.
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Banks advertise savings accounts and CDs with two numbers: the interest rate and the annual percentage yield (APY). The APY includes the effect of compounding, the interest you earn on interest during the year, so it is the number to compare accounts by. This APY calculator converts in both directions and shows what a deposit earns.
APY calculator
APY = (1 + rate / n)^n − 1, where n is the number of compounding periods per year (daily uses 365); continuous compounding uses e^rate − 1. Interest assumes the rate stays the same and no withdrawals. Under Regulation DD (Truth in Savings), banks must state the APY so you can compare accounts.
Key takeaways
- A 4.00% rate compounded daily equals an APY of 4.081%; $10,000 earns about $408.08 in a year.
- The more often interest compounds, the higher the APY, but the difference between daily and monthly compounding is tiny.
- Federal Regulation DD (Truth in Savings) requires banks to disclose the APY, so you can compare accounts on the same basis.
- For loans, the comparable number is the APR, which works differently.
The APY formula
APY = (1 + r ÷ n)n − 1
r is the nominal annual rate and n the number of compounding periods per year: 365 for daily, 12 for monthly, 4 for quarterly. With continuous compounding the formula becomes er − 1. To go from APY back to the rate, the calculator solves the formula for r: r = n × ((1 + APY)1/n − 1). A 4.00% APY with daily compounding corresponds to a 3.922% rate.
How compounding changes the APY
| 4.00% rate compounded | APY | Interest on $10,000 in a year |
|---|---|---|
| Annually | 4.000% | $400.00 |
| Semiannually | 4.040% | $404.00 |
| Quarterly | 4.060% | $406.04 |
| Monthly | 4.074% | $407.42 |
| Daily | 4.081% | $408.08 |
| Continuously | 4.081% | $408.11 |
The step from annual to monthly compounding adds about $7 a year on $10,000; from monthly to daily, less than $1. The rate itself matters far more than the compounding frequency.
APY in the law: Regulation DD
The Truth in Savings Act and its Regulation DD require banks and savings institutions to state the APY in advertising and account disclosures. The rule's formula is based on the interest earned on a deposit over the term and a 365-day year: APY = 100 × [(1 + interest ÷ principal)365 ÷ days in term − 1]. For a full year at a constant rate this matches the compounding formula above. Credit unions follow equivalent NCUA rules.
APY vs. APR vs. interest rate
| Term | Used for | Includes compounding? |
|---|---|---|
| Interest rate (nominal rate) | Savings and loans | No |
| APY (annual percentage yield) | Savings accounts, CDs, money market accounts | Yes |
| APR (annual percentage rate) | Loans and credit cards | No, but includes certain fees |
For a credit card, the APR is the yearly rate before compounding; the effective cost of a balance carried all year is slightly higher. More in how credit card interest is calculated.
Using the APY to compare accounts
- Compare savings accounts and CDs by APY, not by rate.
- Check that the APY applies to your balance; some accounts pay tiers or require minimums.
- Savings APYs are variable; a CD's APY is fixed for the term. See CD vs. high-yield savings.
- Treasury bills quote a yield rather than an APY; compare their coupon-equivalent yield with an APY; see Treasury bills.
Frequently asked questions
Is APY the same as interest rate?
No. The APY includes compounding, so it is slightly higher than the rate unless interest compounds only once a year.
What is a good APY?
Leading high-yield savings accounts paid around 4% APY in October 2026, while the FDIC's national average for savings accounts was 0.37%.
How is interest calculated if I deposit for less than a year?
The calculator scales the APY over your time period: interest = deposit × ((1 + APY)months ÷ 12 − 1).
Is APY earned before or after taxes?
Before taxes. Interest is taxable as ordinary income in the year it is credited.
Why do some banks show APY and others APR on savings?
For deposit accounts, U.S. banks must disclose the APY. An "APR" on a savings ad is usually the nominal rate.
