Convert a nominal APR into the APY you actually earn — or work backwards from an advertised APY to the underlying APR. Pick the compounding frequency and see the exact effect it has on your yield.
📌 APY = (1 + r/n)ⁿ − 1. US banks must advertise APY on deposit accounts, so the number on a savings or CD offer already includes compounding.
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The APY formula
APY = (1 + r/n)n − 1
where r is the APR as a decimal and n is the number of compounding periods per year (365 daily, 12 monthly, 4 quarterly, 1 annually). Worked example: 5% APR compounded monthly is (1 + 0.05/12)12 − 1 = 0.05116 = 5.12% APY. The reverse direction solves for r: APR = n × ((1 + APY)1/n − 1).
As n grows, APY approaches the continuous compounding limit er − 1. At 5% APR that is e0.05 − 1 = 5.127% — only 0.001 percentage points above daily compounding, which is why banks stopping at daily costs you essentially nothing.
Why banks quote APY for savings but APR for loans
APY is always the bigger number, so deposit products are advertised with it; APR is the smaller number, so loans are advertised with that. Both are legally mandated in the US (Truth in Savings for deposits, Truth in Lending for credit), which conveniently matches what looks best in each ad. When you compare products, put them on the same basis first. To see what a given APY does to real dollars over time, try the compound interest calculator, check locked-term earnings with the CD calculator, or plan monthly contributions with the savings calculator.
Frequently asked questions
APR (annual percentage rate) is the nominal yearly rate before compounding. APY (annual percentage yield) is what you actually earn in a year once compounding is included. A 5% APR compounded monthly is a 5.12% APY — the interest earned each month itself earns interest for the rest of the year. For loans it works against you the same way, which is why APY is always at least as high as APR.
Yes, but only marginally. At 5% APR: annual compounding gives exactly 5.00% APY, monthly gives 5.12%, and daily gives 5.13%. The jump from annual to monthly matters; the jump from monthly to daily is worth about a hundredth of a percent. Even the theoretical maximum — continuous compounding, e^0.05 − 1 = 5.127% — barely beats daily. Compare the APY itself, not the frequency.
It moves with Federal Reserve rates, so there is no fixed number. A useful rule of thumb: a competitive high-yield savings account or CD pays an APY close to the current federal funds rate, while big traditional banks often pay a tiny fraction of it. Compare your rate against the best nationally available online-bank offers — if yours is far below, switching is usually worth it.
Most US savings accounts and CDs compound daily and credit the interest monthly. Some banks compound monthly or quarterly. It matters less than it sounds: since banks are required to advertise APY, the compounding is already baked into the number they quote — a 4.50% APY pays the same yearly yield regardless of how it is compounded internally.
Marketing plus regulation. APY is the larger number, so it makes savings products look better; APR is the smaller number, so it makes loans look cheaper. US Truth in Savings rules require APY on deposit accounts, and Truth in Lending requires APR on loans — so to compare a loan APR against a savings APY fairly, convert one of them with this calculator first.