APR — the nominal annual rate — ignores compounding; APY includes it. A deposit quoted at 4.75% compounded monthly actually yields 4.855% over a year, because each month's interest starts earning interest of its own. That gap between the stated rate and the effective yield is the entire difference, and the APY Calculator converts any rate at every compounding frequency; this guide explains what the two labels mean and when each one is the right comparison.
Two labels, two jobs
The labels live on opposite sides of the bank, and each is required by its own disclosure law. Deposit accounts — savings, money markets, CDs — must disclose APY under Truth in Savings (Regulation DD), precisely so that two accounts compounding on different schedules can be compared on a single effective number. Loans must disclose APR under Truth in Lending (Regulation Z), a cost rate that folds certain finance charges in with the interest, so that two loans can be compared on a single cost number. Confusion starts when the two are treated as rivals for the same job. APY answers "what will a deposit effectively earn in a year?" APR answers "what does this credit effectively cost per year, fees included?" Neither answers the other's question.
One vocabulary caution: on a deposit disclosure, the nominal rate is sometimes itself labelled the interest rate, and the word APR gets used loosely for it in everyday speech — that nominal rate is the input to the conversion below. On a credit card or loan, APR is the formal Regulation Z figure. The math on this page converts a nominal rate to an effective yield; it does not recompute any lender's disclosed APR.
The conversion formula
For interest compounded a fixed number of times a year, the conversion is one line:
- APY = (1 + r ÷ n)n − 1, where r is the nominal annual rate and n is the number of compounding periods per year.
- For continuous compounding — the mathematical limit as n grows without bound — APY = er − 1.
Two consequences fall straight out of the formula. First, APY can never be less than the nominal rate: with annual compounding (n = 1) the two are exactly equal, and every increase in frequency pushes the yield up. Second, the gains flatten as frequency rises — each extra compounding acts on a balance boost smaller than the last — so the step from annual to monthly is worth far more than the step from daily to continuous, which at most rates is a difference in the third decimal place.
Worked example — $8,000 at 4.75%, compounded monthly, for 2 years
Nadia deposits $8,000 in an account paying a 4.75% nominal rate, compounded monthly, and leaves it untouched for 2 years (assumptions: the rate never changes, and no fees, taxes, deposits, or withdrawals apply):
- APY: (1 + 0.0475 ÷ 12)12 − 1 = 4.855%
- End of year 1: $8,000 × (1 + 0.0475 ÷ 12)12 = $8,388.38 — $388.38 of interest
- End of year 2: $8,000 × (1 + 0.0475 ÷ 12)24 = $8,795.62 — $407.24 of interest in year 2 alone
- Total interest: $795.62 — and note year 2 earned more than year 1 at the same rate: that growth in the interest itself is compounding, made visible
The same 4.75% at every frequency shows how much of the yield is the compounding schedule rather than the rate:
- Annual: APY 4.750% — $8,778.05 after 2 years ($778.05 of interest)
- Semi-annual: APY 4.806% · Quarterly: APY 4.835%
- Monthly: APY 4.855% — $8,795.62 after 2 years, $17.57 more than annual compounding
- Daily: APY 4.864% — $8,797.22 after 2 years, just $1.60 more than monthly
- Continuous: APY 4.865% — the ceiling daily compounding approaches
The lesson of the ladder: compare accounts on APY and the whole schedule difference collapses into one honest number — but expect frequency, on its own, to be worth dollars and cents, not a fortune. Rate differences move the outcome; frequency differences polish it.
Try it with your own numbers
This mini-calculator is prefilled with the worked example above and runs the same conversion as the full tool. The full calculator also prints the APY at every compounding frequency side by side and a year-by-year growth table.
Result
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| Balance at the end | — |
| Total interest earned | — |
Open the full calculator — the APY Calculator runs the complete version of this calculation.
The borrowing side: what a loan's APR is doing
A loan's APR is not simply the note rate with a new name — Regulation Z builds certain finance charges into it, which is why a loan's APR can sit above its interest rate. The interest itself is still computed from the amount financed, the rate, and the term, by the standard amortization formula. Borrow $24,000 — the amount financed — at 7.5% APR for 48 months and the payment is $580.29 a month, $27,854.10 paid in total, of which $3,854.10 is interest — the figures the Auto Loan Calculator builds once its purchase worksheet, taxes and fees included, settles on that amount financed. And the two labels meet in one instructive comparison: if that same 7.5% were a nominal deposit rate compounded monthly, its effective yield would be (1 + 0.075 ÷ 12)12 − 1 = 7.763%. Same digits, different statement — the borrowing figure describes a cost with charges folded in, the deposit figure describes a yield with compounding counted.
Credit cards sit closest to the boundary. A card's APR is the nominal annual rate from which each month's interest is figured — balance × APR ÷ 12 in the simplified simulation — so the APR is what drives a balance's cost month to month, which is exactly the machinery behind the minimum payment calculation: the rate on the statement, applied again and again to whatever balance remains.
Which number to compare, and when
Comparing two savings accounts or CDs: use APY — it is the one figure that already contains each account's compounding schedule. Comparing two loans: use APR as the starting point, then read the total interest over the term, because APR comparisons assume you hold the loan to its end. What never works is crossing the aisle: a savings APY set against a loan APR compares a yield that excludes fees with a cost that includes them, on balances that usually differ, and the subtraction means less than it appears to. Each label is a fair comparison inside its own category and a misleading one outside it.
For educational and planning purposes only — not financial advice. This guide explains the standard definitions and conversion formulas with a simplified example (fixed rate, no fees, taxes, deposits, or withdrawals); real accounts compound and credit on schedules set by the bank, and lenders disclose APR under rules that decide which charges are included. It is not professional financial advice. Verify the rate, APY, and APR for any real account or loan against the lender's or bank's own statements and disclosure documents before acting.