APY calculator
Rate conversion
Convert between a nominal annual rate and annual percentage yield.
Optional balance estimate
Estimate growth from the converted APY without recurring deposits or withdrawals.
Dollar estimates assume the principal remains deposited and the APY stays constant for the term.
Compounding comparison
Rows use the same equivalent nominal annual rate so the APY effect is easier to compare.
| Frequency | APY | APY lift |
|---|---|---|
| Annual | 5% | 0 bp |
| Semiannual | 5.0625% | +6.2 bp |
| Quarterly | 5.0945% | +9.5 bp |
| Monthly | 5.1162% | +11.6 bp |
| Daily | 5.1267% | +12.7 bp |
| Continuous | 5.1271% | +12.7 bp |
Formula and methodology
APY from a nominal annual rate is calculated as (1 + r / n) ^ n - 1, where
r is the nominal annual rate and n is the number of compounding periods per
year. Continuous compounding uses e ^ r - 1.
APY to nominal rate
The reverse conversion solves for the nominal annual rate that produces the entered APY at the selected
frequency. Continuous compounding uses the natural log of 1 + APY.
Important assumptions
Optional dollar estimates use the converted APY only. They assume the principal stays deposited for the term and exclude deposits, withdrawals, fees, taxes, bonuses, promotional windows, and rate changes.
APY versus nominal rate
A nominal annual rate is the stated rate before compounding. APY is the effective one-year yield after compounding, so monthly, daily, and continuous compounding can produce a higher APY from the same nominal rate.
No live rates or advice
This browser-side calculator does not rank banks, connect to accounts, use live savings or CD rates, or provide personalized financial advice. Account disclosures can use special APY rules for tiered, stepped, or time accounts.
Need help?
See the APY calculator help page for inputs, methodology, FAQ, and troubleshooting.
Related calculators
Compare this topic with the Compound interest , Investment , Debt payoff pages.
APY vs nominal rate, explained
Two numbers can describe the same account: the nominal annual rate the interest is calculated from, and the annual percentage yield (APY) the money actually earns over a year once compounding is included. Confusing them makes offers look better or worse than they are, and the gap between them is pure compounding frequency.
The conversion formula
APY equals (1 + r / n) ^ n - 1, where r is the nominal annual rate and
n is the number of compounding periods per year. Dividing the rate into more, smaller
pieces lets each piece earn on the previous ones, which is why APY is always at least the nominal rate.
The full mechanics are covered on the
compound interest calculator page.
Same nominal rate, different APY
A 5% nominal annual rate produces a 5.000% APY with annual compounding, about 5.095% quarterly, 5.116% monthly, 5.127% daily, and 5.127% at the continuous limit. The biggest jump comes from compounding at all; moving from monthly to daily adds only a basis point or two. That is why two banks quoting "5%" can legitimately pay slightly different amounts of interest.
Which number banks quote and why
US deposit accounts advertise APY because regulation requires a figure customers can compare directly, regardless of each bank's compounding schedule. Rate sheets and disclosures may still mention the nominal ("interest") rate. When comparing savings accounts or CDs, compare APY to APY; this calculator converts in either direction when an offer only states one of the two.
APY vs APR on debt
APR on loans and credit cards is a nominal-style annual rate, typically not compounded in the quoted figure. A card's 22% APR applied monthly behaves like roughly 24.4% effective annual cost — the same conversion this calculator performs, just working against you. That gap is one reason high-APR balances grow faster than people expect; the debt payoff calculator shows what it takes to reverse it, and the investment calculator shows the same compounding working in your favor. For the full comparison of the two quoted rates, read APY vs APR: What The Difference Costs You.