Saving & investing
APY Calculator
Convert a nominal rate to APY (AER) or back for any compounding, continuous included, or find the APY an account paid from its interest and days.
Annual percentage yield (APY)
5.116%
from 5% compounded monthly
APY as a bank discloses it
5.12%
Rounded to two decimals, as US Truth in Savings requires
Nominal rate
5%
compounded monthly
What compounding adds
0.116 points
APY minus the nominal rate
How 5.116% was worked out
With 12 credits a year at 5% ÷ 12 each, a year returns (1 + 0.05 ÷ 12)^12 − 1 = 5.1162%.
A constant rate for a full year. An estimate, not financial advice, providers may calculate differently.
5% at every compounding frequency
| Compounding | Nominal rate | APY |
|---|---|---|
| Yearly | 5% | 5% |
| Half-yearly | 5% | 5.062% |
| Quarterly | 5% | 5.095% |
| Monthly (yours) | 5% | 5.116% |
| Weekly | 5% | 5.125% |
| Daily | 5% | 5.127% |
| Continuous | 5% | 5.127% |
Two accounts are only comparable on their APY: the same nominal rate is worth more the more often it is credited, though the step from daily to continuous is a fraction of a hundredth of a point.
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How this is calculated
A nominal rate is divided among the times a year interest is credited, and each credit then earns interest of its own, so a full year returns more than the headline percentage; that larger figure is the APY, or AER in Britain. The calculator converts in either direction for yearly, half-yearly, quarterly, monthly, weekly, daily or continuous compounding, and in its third mode it annualises the interest a deposit actually paid over its term with the formula US banks must use for their disclosures. The table under the result lists the same rate at every frequency, so two accounts quoted on different schedules can be set side by side.
APY(1 + r ÷ m)m − 1
- r
- the Nominal annual rate as a decimal
- m
- the times a year the Compounding setting credits interest
What this does not include
- Fees and minimum-balance charges, which reduce what an account really yields.
- Tax on interest.
- Rate changes: the conversion assumes one rate for a full year.
- Tiered rates; work out each tier's balance separately.
How this calculator works
APY and nominal rates: converting them and reading a bank's figure. The compounding formulas behind APY and AER, how to run them backwards, the Truth in Savings formula for a deposit's real yield, and three worked examples.
This calculator is for general information only and is not financial advice. Results are estimates based on the figures you enter and the stated formula; lenders and providers may round or calculate differently. Check any decision with the institution involved or a qualified adviser.