What this page sets up
The calculator opens solving for the yield: 10,000 that grew to 10,400 in one year, compounded daily, which is an APY of 4.00%. Put in your own starting balance, the balance it reached and how long it took. For a statement period, choose Between dates and pick the first and last day: with 365 days a year this is the Regulation DD formula for the annual percentage yield earned, (1 + interest ÷ balance)^(365 ÷ days) − 1.
To go the other way, from a nominal rate to its APY, switch Calculate to Final balance, set The rate is to Nominal rate (APR), and enter the rate and its compounding. The APY appears in the stats under the result, and Formulas with your numbers shows the working.
Reading the result
The large figure is the APY the growth works out to. The simple interest card shows the flat yearly rate that would give the same growth with no compounding, which is always higher than the nominal rate needed with compounding. When there are deposits along the way, the calculator solves for the single rate that grows all of them to the target, the way a savings plan’s yield is worked out.
Using APY to compare accounts
- Check your statement against the offer. Put the statement’s opening balance, the interest credited and the statement dates into Between dates: the result is the APY you actually earned, to set against the APY you were promised.
- Convert before comparing with a loan. A loan’s APR is defined differently and includes some fees; it isn’t the same measure as a deposit’s APY.
- Use the right period. An APY is a yearly figure. Over 3 months, 10,000 at 4.00% APY earns about 98.53, not 100, because the yield compounds.
To plan a savings balance at a given APY, use the high-yield savings calculator.
APY for each rate and compounding frequency
The yield of a nominal annual rate (APR) once compounding is included, APY = (1 + r/n)^n − 1, or e^r − 1 for continuous compounding. Daily uses 365 days.
| Nominal rate | Annually (1/yr) | Quarterly (4/yr) | Monthly (12/yr) | Daily | Continuously |
|---|---|---|---|---|---|
| 1% | 1% | 1.004% | 1.005% | 1.005% | 1.005% |
| 2% | 2% | 2.015% | 2.018% | 2.02% | 2.02% |
| 3% | 3% | 3.034% | 3.042% | 3.045% | 3.045% |
| 4% | 4% | 4.06% | 4.074% | 4.081% | 4.081% |
| 5% | 5% | 5.095% | 5.116% | 5.127% | 5.127% |
| 6% | 6% | 6.136% | 6.168% | 6.183% | 6.184% |
| 8% | 8% | 8.243% | 8.3% | 8.328% | 8.329% |
| 10% | 10% | 10.381% | 10.471% | 10.516% | 10.517% |
From an APY back to the nominal rate
The rate a bank would state for the same yield, r = n × ((1 + APY)^(1/n) − 1):
| APY | Nominal rate, compounded monthly | Nominal rate, compounded daily |
|---|---|---|
| 1% | 0.9954% | 0.995% |
| 2% | 1.9819% | 1.9803% |
| 3% | 2.9595% | 2.956% |
| 4% | 3.9285% | 3.9223% |
| 4.5% | 4.4098% | 4.402% |
| 5% | 4.8889% | 4.8793% |
| 6% | 5.8411% | 5.8274% |
Source: CFPB, Regulation DD (Truth in Savings), Appendix A, the APY and APY-earned formulas. Not financial advice.