APR is the rate, APY is what you earn
Banks advertise savings accounts and CDs by their APY (annual percentage yield) because it is the bigger, more honest number: it includes the effect of compounding. The APR (or nominal rate) is the rate before compounding. This calculator converts one into the other and projects what an account earns, including regular monthly deposits.
The formula
APY = (1 + APR ÷ n)ⁿ − 1
where n is the number of compounding periods per year: 365 for daily, 12 for monthly, 4 for quarterly, 1 for annual.
To project a balance with monthly deposits, the calculator turns the APY into an equivalent monthly rate, (1 + APY)^(1/12) − 1, and applies the future value formula to the opening deposit and to each monthly deposit.
Worked example: 4% APR compounded daily
- APY: (1 + 0.04 ÷ 365)³⁶⁵ − 1 = 4.081%.
- With monthly compounding the APY would be 4.074%; with annual compounding, exactly 4%.
- You open the account with $10,000 and add $200 a month for one year.
- Ending balance: about $12,852.65.
- You deposited $12,400, so interest earned is $452.65.
- Interest in the first month alone: about $33.39.
Daily compounding adds less than a tenth of a point here. The rate itself matters far more than the compounding frequency.
Balance after one year by rate
| APR | APY (daily) | Ending balance | Interest earned |
|---|---|---|---|
| 0.5% | 0.501% | $12,455.63 | $55.63 |
| 2% | 2.020% | $12,624.15 | $224.15 |
| 3% | 3.045% | $12,737.85 | $337.85 |
| 4% | 4.081% | $12,852.65 | $452.65 |
| 4.5% | 4.602% | $12,910.47 | $510.47 |
| 5% | 5.127% | $12,968.56 | $568.56 |
The gap between a traditional savings account paying a fraction of a percent and a high-yield account is roughly $400 a year on this balance.
Where APY applies
- High-yield savings and money market accounts: variable APY that moves with Federal Reserve rate decisions.
- Certificates of deposit (CDs): fixed APY for a set term, with a penalty for early withdrawal.
- Treasury bills are quoted differently (discount yield or investment rate) but can be compared on an APY basis.
The Truth in Savings Act requires banks to disclose APY, so you can compare accounts on the same footing.
Taxes and insurance
Interest from a bank account is taxable as ordinary income in the year it is credited, and your bank reports it on Form 1099-INT once it reaches $10. Treasury interest is exempt from state and local income tax. Deposits are insured by the FDIC (or NCUA for credit unions) up to $250,000 per depositor, per bank, per ownership category.
Inflation check
A 4% APY with 3% inflation is roughly a 1% real return. Savings accounts are for safety and short-term goals; long-term growth usually needs investments with higher expected returns and more risk.