APY Calculator
Find the annual percentage yield of any interest rate and compounding frequency, then see how a savings account grows with monthly deposits, year by year.
Balance by year
Year-by-year growth
| Year | Deposits | Interest | Total interest | Balance |
|---|
APY by compounding
| Compounding | APY |
|---|
Reverse: APY → APR
Nominal rate (monthly): –
Contributions are added at the end of each month. Interest is applied at the monthly rate equivalent to the APY, so any compounding frequency is handled consistently. Taxes and fees are not included.
How to use the APY Calculator
- Enter the interest rate (the nominal rate or APR) of your savings account, CD or bond.
- Choose how often interest compounds: daily, monthly, quarterly, semi-annually, annually or continuously.
- Add your initial deposit, monthly contribution and the number of years.
- Press Calculate APY to see the yield, final balance, interest earned, chart and yearly table.
- Use the reverse box to turn an advertised APY back into its nominal rate.
APY formula
APY (annual percentage yield) is the interest you actually earn in one year once compounding is included. For a nominal rate r compounded n times a year:
- APY = (1 + r ÷ n)n − 1
- Continuous compounding: APY = er − 1
- Reverse (APY to APR): r = n × ((1 + APY)1/n − 1), or r = ln(1 + APY) for continuous compounding.
Worked example
A savings account pays 4.5% compounded monthly. You open it with 10,000 and add 200 at the end of every month for 10 years.
- APY = (1 + 0.045 ÷ 12)12 − 1 = 4.594%.
- Balance = 10,000 × 1.00375120 + 200 × (1.00375120 − 1) ÷ 0.00375 ≈ 45,909.54.
- You deposited 34,000, so the interest earned is about 11,909.54.
How compounding changes APY at 4.5%
| Compounding | Times per year | APY | Interest on 10,000 in a year |
|---|---|---|---|
| Annually | 1 | 4.5000% | 450.00 |
| Semi-annually | 2 | 4.5506% | 455.06 |
| Quarterly | 4 | 4.5765% | 457.65 |
| Monthly | 12 | 4.5940% | 459.40 |
| Daily | 365 | 4.6025% | 460.25 |
| Continuous | ∞ | 4.6028% | 460.28 |
More frequent compounding raises the yield, but the gain shrinks quickly: going from monthly to daily adds less than a hundredth of a percentage point. When comparing savings accounts, compare their APYs, not their nominal rates.
Frequently asked questions
What is APY?
APY, or annual percentage yield, is the real rate of return on a deposit over one year, including the effect of compounding. A 4.5% rate compounded monthly has an APY of 4.594%, because interest earned each month also earns interest.
How do you calculate APY?
Use APY = (1 + r/n)^n − 1, where r is the nominal annual rate as a decimal and n is the number of compounding periods per year. For 5% compounded daily: (1 + 0.05/365)^365 − 1 = 5.127%.
What is the difference between APY and APR?
APR is the simple nominal yearly rate without compounding. APY includes compounding, so it is always equal to or higher than the APR. Banks quote APY on savings to show what you earn and APR on loans to show what you pay.
Is a higher compounding frequency better?
Yes, but only slightly. At 4.5%, monthly compounding gives 4.594% APY and daily compounding 4.602%. The interest rate itself matters far more than how often it compounds.
How much will I earn in a high-yield savings account?
Multiply your balance by the APY for a rough yearly figure: 10,000 at 4.5% APY earns about 450 in a year. With regular deposits, use the calculator to project the balance over several years.
How do I convert APY to APR?
Reverse the formula: APR = n × ((1 + APY)^(1/n) − 1). A 5% APY with monthly compounding equals a nominal rate of about 4.889%.