How to use the APY calculator
The page has two tools.
APR to APY converts between the stated rate and the yield.
- Choose the direction. “Interest rate → APY” when you know the nominal rate; “APY → interest rate” when you know the APY and want the rate behind it.
- Enter the rate as a percentage: 4.5 for 4.5%.
- Choose the compounding frequency, which is in the account’s disclosure. Most US online savings accounts compound daily and credit interest monthly.
The table shows the same rate at every compounding frequency, and the chart shows how the gap between APY and the stated rate widens as rates rise.
Compare accounts ranks savings accounts by what you would actually have at the end.
- List the accounts. For each one, enter a name, the stated (nominal) rate, how many times a year it compounds (365 for daily, 12 for monthly, 4 for quarterly, 1 for annually), and any monthly fee. Leave the fee empty if there is none.
- Enter the deposit and the number of years.
The best account is highlighted in green. If an account’s fees exceed its interest, it is flagged in red.
The APY formula
Continuous compounding: APY = er − 1r is the nominal annual rate as a decimal and n the number of compounding periods per year: 365 daily, 12 monthly, 4 quarterly, 1 annually.
Going the other way, the nominal rate that produces a given APY is:
Continuous compounding: r = ln(1 + APY)
In the account comparison, each account’s balance grows every month by (1 + r ÷ n)n/12, and any monthly fee is subtracted at the end of the month. The effective yield after fees is the annual rate that would turn the deposit into the ending balance: (ending balance ÷ deposit)1/years − 1.
Worked examples
Rate to APY. A savings account pays 4.5% compounded daily. The APY is 4.602%, so $10,000 left for a year earns $460.25 rather than $450.00.
APY to rate. A bank advertises 5% APY with monthly compounding. The nominal rate behind it is 4.889%. With annual compounding, the nominal rate and the APY would be the same: 5.000%.
Comparing accounts. You have $10,000 for 3 years. The example lists four accounts; the winner is Online savings with $11,359.76, ahead of Credit union by $13.50.
How much does compounding frequency matter?
For a 4.5% nominal rate:
| Compounding | APY |
|---|---|
| Annually | 4.500% |
| Quarterly | 4.577% |
| Monthly | 4.594% |
| Daily | 4.602% |
| Continuously | 4.603% |
The steps get smaller as compounding gets more frequent: daily and continuous compounding are almost identical. The effect also depends on the rate. At 1%, daily compounding adds only 0.01% to the yield; at 10% it adds 0.52%, measured in percentage points. At today’s savings rates, the frequency is a tie-breaker, not a reason to choose an account.
Reading the account comparison
The example deliberately includes accounts that look similar on paper:
| Account | Stated rate | APY | Fees over 3 years | Balance after 3 years |
|---|---|---|---|---|
| Online savings | 4.25%, daily | 4.34% | $0.00 | $11,359.76 |
| Credit union | 4.30%, annually | 4.30% | $0.00 | $11,346.27 |
| Money market | 4.50%, monthly | 4.59% | $180.00 | $11,250.15 |
| Branch savings | 0.50%, monthly | 0.50% | $0.00 | $10,151.10 |
Three lessons come out of it. First, the credit union’s higher stated rate loses to the online account’s daily compounding, because 4.25% compounded daily is a higher APY than 4.30% compounded once a year. Second, the money market account has the best APY of the four, but a $5 monthly fee turns that into the third-best result: its effective yield after fees is 4.00%. Fees are flat dollar amounts, so they hurt most on small balances; with $50,000 instead, the money market account finishes first, at $57,020.06. Third, the gap between a competitive account and a typical branch account, $1,208.67 over three years here, dwarfs every other difference in the table.
Over 10 years, the best account in the example would reach $15,295.53.
What this calculator does not include
- Rate changes. Savings and money market rates are variable. A comparison over several years assumes today’s rates hold, which they rarely do.
- Introductory rates and balance tiers. Some accounts pay a promotional rate for a few months, or the top rate only up to a balance cap. Model these by entering the rate you expect on average.
- Taxes. Interest is taxable in the US as ordinary income, except on Treasury securities, which are exempt from state and local tax. The tax-equivalent yield calculator puts such yields on an equal footing.
- Deposit insurance and access. FDIC or NCUA insurance, withdrawal limits and transfer times are not reflected in the numbers but matter for where you keep cash.
To project a balance with regular deposits, use the savings calculator; for money you can lock away for a fixed term, the CD calculator.