APY is the rate you actually earn once compounding counts, so it always meets or beats the nominal rate: a 5.00% nominal rate compounded monthly is a 5.116% APY, daily is 5.127%, and on a $10,000 deposit held 3 years at the monthly figure the balance reaches $11,614.72 — $1,614.72 of interest.
APY vs the nominal rate (APR)
Every savings account and CD disclosure carries two rates. The nominal rate — labelled APR on many disclosures, and the field name on this page — is the stated annual rate before compounding: it says what interest is charged on the balance at each compounding, and nothing about what those compoundings add up to. The APY, the annual percentage yield, is the effective rate after a full year of compounding is counted. United States banks must disclose APY under Regulation DD, the Truth in Savings rules, precisely so two accounts with different compounding schedules can be compared on one number. One caution about vocabulary: the APR on a loan is a different disclosure that folds in fees; the APR field here means only the stated nominal deposit rate, with no fees anywhere in the math.
Compounding frequency — and why the gains flatten
Compounding is interest earning interest: each time interest is credited, the next period's interest is figured on a slightly larger balance. More frequent compounding therefore pays more — but each step up pays less than the one before, because the balance boost from each extra compounding is itself smaller. The ladder at a 5.00% nominal rate, which the tool above reproduces at whatever rate you enter, shows the shape:
| Compounding at 5.00% nominal | APY |
|---|---|
| Annual | 5.000% |
| Semi-annual | 5.063% |
| Quarterly | 5.095% |
| Monthly | 5.116% |
| Daily | 5.127% |
| Continuous | 5.127% |
Daily and continuous tie at three decimal places here, and the tie is honest, not a rounding trick: the true values are 5.1267% and 5.1271%. Continuous compounding is the mathematical limit that daily compounding approaches, so the difference between them lives in the fourth decimal — and, over long terms, in the growth dollars. This page displays APY to three decimals everywhere, because at two decimals monthly and daily sit a misleading 0.01 apart and daily and continuous collapse into the same figure.
Worked example — 5.00% monthly, $10,000 for 3 years
The calculator is pre-filled with exactly this case:
- APY: (1 + 0.05/12)12 − 1 = 5.116% (at bank-style 2 dp, the familiar 5.12%)
- End balance: $10,000 × (1 + 0.05/12)36 = $11,614.72; total interest $1,614.72
- Year 1: balance $10,511.62, interest that year $511.62
- Year 2: balance $11,049.41, interest that year $537.79
- Year 3: balance $11,614.72, interest that year $565.31
The yearly table evaluates the growth formula itself at each whole year — it never compounds the displayed, rounded APY — and the interest-that-year column sums to the total: $511.62 + $537.79 + $565.31 = $1,614.72.
Finding your frequency, and reading the dollars
Your account's compounding frequency is stated in its disclosure documents — the account agreement and the rate sheet — rather than on marketing pages, which usually quote only the APY. CDs and savings accounts compound on a variety of schedules set by the bank; there is no single schedule to assume, which is why the frequency is an input here rather than a hidden default. As for reading the outputs: the APY percentage is the comparison tool — it puts accounts with different schedules on one scale — while the dollar table is the planning tool, showing what a specific deposit becomes over a specific term. A higher APY on a small balance can be worth fewer dollars than a lower APY on a large one, and the table is where that becomes visible.
Reading the yearly table
The growth table reports the balance at the end of each whole year of the term, with the interest earned during that year beside it. Two things about it are worth noticing. First, the interest column grows even though the rate never changes — $511.62 in year one, $537.79 in year two, $565.31 in year three of the worked example — because each year's interest is figured on a balance that includes every earlier year's interest. That growth in the interest itself, not any change in the rate, is compounding made visible. Second, the column is a check on the headline figures: the interest-that-year amounts always sum to the total interest printed above the table, to the cent, because every row comes from the same formula evaluated at a different year. A fractional final term — 2.5 years, a common CD length — gets whole-year rows for years one and two and a final row labelled with the exact term, carrying the end balance, so the last row of the table is always the answer the summary lines report.
What the calculation leaves out
The formulas assume the rate stays constant for the whole term, and real accounts do not promise that outside a fixed-rate CD. They also leave out fees, which reduce an effective yield; taxes on the interest; and, for CDs, early-withdrawal penalties, which can erase months of interest if the money leaves early. Additional deposits and withdrawals are not modelled — this page grows a single deposit. None of that makes the conversion wrong; it makes it a conversion. The figure to hold an actual account to is the APY in its own disclosure, and this tool's job is to let you reproduce and explore that figure, not to replace it.