Effective APY Calculator
Convert any quoted nominal interest rate into a true Annual Percentage Yield (APY) based on how often it compounds. See exactly how 4.50% APR with monthly compounding compares to 4.50% APR daily.
Effective annual yield (APY)
4.6%
Balance after horizon
$12,518
APY premium over nominal APR
0.1%
Total interest earned
$2,518
If it were simple interest (no compounding)
$12,250
Balance Growth — Compounding vs. Simple Interest
How to read your result
The 'Effective annual yield (APY)' is the true rate your money compounds at over a year, taking the quoted nominal rate and the compounding frequency into account. It is always greater than or equal to the nominal rate — equal only when interest compounds once a year.
The 'APY premium over nominal APR' is the gap between the two. At a 4.50% nominal rate, monthly compounding adds roughly 0.094 percentage points (4.594% APY). Daily compounding adds about 0.102 points. The premium grows as the nominal rate rises — at 10% nominal, monthly compounding adds about 0.47 points.
'Balance after horizon' shows what the starting balance grows to using the effective compounding schedule. Compare it to 'If it were simple interest' to see the dollar value of compounding for your specific rate, balance, and time horizon. The gap is small at year 1 and dramatic at year 30.
The chart visualizes the divergence between compound and simple interest. Below ~5% nominal and short horizons (under 5 years), the two lines look nearly identical. Past 10 years, the compounded line bends visibly upward — that's compounding doing the work.
When to use this tool
- ›Comparing two HYSA or CD offers where one quotes APR and the other quotes APY. Plug each one into this calculator with its compounding frequency to see which actually pays more.
- ›Sanity-checking a savings or investment offer that advertises a high nominal rate but only compounds annually — the APY ends up identical to the APR, which can change the comparison.
- ›Estimating the difference between daily and monthly compounding. For most US savings accounts, daily compounding adds only a few basis points over monthly — usually not the deciding factor.
- ›Translating a credit-card APR into the effective APY you'd actually owe if you carried a balance for a year (most cards compound daily on average daily balance).
Methodology
The effective APY formula is the standard textbook conversion: APY = (1 + r/n)^n − 1, where r is the nominal annual rate (as a decimal) and n is the number of compounding periods per year. At n = 1, APY equals the nominal rate.
Final balance uses the same compounding schedule extended over the full horizon: balance = principal × (1 + r/n)^(n × years). 'Simple interest' is shown for comparison only — most real savings products compound, so the simple line is a counterfactual.
Common compounding frequencies: 1 (annual), 4 (quarterly), 12 (monthly), 365 (daily). Continuous compounding (e^(rt)) is mathematically the limit and adds about 0.013 points to a 5% rate over daily compounding — usually irrelevant for retail savings.
Limits we acknowledge: this calculator does not model variable rates, intra-year deposits or withdrawals, or tax drag. Bank disclosures use the same formula but may compound on the daily balance rather than at fixed intervals, which can cause small (≤0.01%) differences in practice.
Site-wide methodology framework: /methodology/ · Pre-publication standards: /editorial-standards/
FAQ
Is APY always higher than the nominal rate (APR)?
APY is greater than or equal to APR — never less. They are equal only when compounding happens exactly once per year. Any more frequent compounding produces a higher APY. The gap grows with both the nominal rate and the compounding frequency, but tops out near continuous compounding (e^r − 1).
Why do banks quote APY for savings but APR for loans?
Regulation. The US Truth in Savings Act requires banks to quote savings products in APY because that's the figure consumers earn. The Truth in Lending Act requires loans to quote APR (without compounding effects) so consumers can compare loan costs. Both numbers describe the same underlying math, but viewed from different sides of the transaction.
Does daily compounding really matter compared to monthly?
Almost never enough to be the deciding factor. At a 4.50% nominal rate, monthly compounding gives 4.594% APY and daily gives 4.602% — a 0.008-point difference, or about $4 per year on a $50,000 balance. Choose the account based on the nominal rate, fees, and access; the compounding-frequency difference is rounding error.
Why is this different from the Compound Interest Calculator?
The Compound Interest Calculator focuses on growth over time given a single rate and frequency. This tool focuses specifically on the conversion between APR and APY at a single point in time, plus a side-by-side simple-vs-compound chart. Use this one to compare offers; use the compound-interest tool to project a balance with regular contributions.
What number should I use for credit-card balances?
Most credit cards compound daily on the average daily balance, so plug in 365 for compounding frequency. The card's quoted APR (e.g., 22.99%) becomes a 25.84% APY at daily compounding — meaningfully higher than the headline number. This is why carrying a balance is more expensive than the APR alone implies.
Why is the chart's compounding line indistinguishable from the simple line at short horizons?
Because compounding's effect is back-loaded. Year 1's gap is just the difference between the nominal rate and the APY (a few basis points at typical savings rates). The two lines diverge visibly after about year 7 at 5% nominal rates, and dramatically past year 20. Time is the dominant variable, not the compounding frequency.