APY Calculator
Convert a nominal interest rate to its annual percentage yield and back at any compounding, or find the APY of an account from the interest it paid.
Result
Annual percentage yield: 5.1162%
Arithmetic on the rate or interest you enter. An account’s own disclosure is what the bank must honour.
- Nominal annual rate
- 5%
- Rate each compounding period
- 0.4167%
https://calcgallery.com/time-value/apy-calculator/
Results are arithmetic on the returns, rates and horizons you enter, not a forecast and not investment, tax or retirement advice. The site supplies no expected return, inflation rate, contribution limit, tax rate or withdrawal rate. Real returns vary from year to year, and fees, taxes and the order of returns all change the outcome. Check anything that matters with a qualified adviser. Read the full disclaimer
How to use the APY Calculator
- Choose whether you have a nominal interest rate, an APY, or the interest an account actually paid.
- Enter the rate and how often interest is added, or the deposit, the interest and the days in the term.
- Read the annual percentage yield, or the nominal rate that produces the APY you entered.
The formulas
A nominal rate r with interest added m times a year gives:
APY = (1 + r/m)^m − 1continuous compounding: APY = e^r − 1Going the other way, the nominal rate that produces a given APY is m × ((1 + APY)^(1/m) − 1), or ln(1 + APY) for continuous compounding. Daily compounding uses 365 days.
APY from the interest an account paid
Regulation DD, which governs how US deposit accounts disclose their yield, defines the APY from what an account actually pays:
APY = (1 + interest ÷ principal)^(365 ÷ days in term) − 1Days in the term are the actual days: 182 for a typical six-month CD, 730 for two years. For a term of exactly 365 days the formula reduces to the interest divided by the principal. This is the version to use when a CD’s rate changes during the term, because it works from the total interest paid rather than from any one rate.
Comparing accounts
APY puts accounts that compound differently on the same footing, which is why US banks must quote it. Compare APY with APY. A higher nominal rate compounded less often can still yield less than a lower rate compounded more often.
With your numbers
- APY = (1 + 5% ÷ 12)^12 − 1 = 5.1162%
Quick reference
Arithmetic on the rate or interest you enter. An account’s own disclosure is what the bank must honour.
| Example | Result |
|---|---|
| 5% compounded monthly | Annual percentage yield: 5.1162% |
| 5% compounded daily | Annual percentage yield: 5.1267% |
| 5% compounded continuously | Annual percentage yield: 5.1271% |
| A 5% APY as a monthly rate | Nominal annual rate: 4.8889% |
| 30.37 earned on 1,000 over 182 days | Annual percentage yield: 6.1837% |
| 133.13 earned on 1,000 over two years | Annual percentage yield: 6.4486% |
| 3.5% compounded quarterly | Annual percentage yield: 3.5462% |
Common questions about the APY Calculator
- What is the difference between APY and the interest rate?
- The interest rate, also called the nominal rate, is the yearly rate before compounding. The APY is what the account actually earns in a year once interest is added to the balance and itself earns interest. 5% compounded monthly adds 0.4167% a month, which grows to an APY of 5.1162%.
- How do banks calculate APY?
- In the US, Regulation DD sets the formula: one plus the interest earned divided by the deposit, raised to the power of 365 divided by the days in the term, minus one. Choose "The interest an account paid" to use it. With the regulation’s own example, 30.37 of interest on 1,000 over 182 days gives 6.18%.
- Does daily compounding earn much more than monthly?
- Only a little. At 5%, monthly compounding gives 5.1162% and daily 5.1267%. Even continuous compounding, the limit of adding interest ever more often, only reaches 5.1271%.
- Is APY the same as APR?
- No. APY describes what a deposit earns, including compounding. APR describes what a loan costs, including certain fees, and in the US it is not compounded. The two are defined by different regulations for different purposes.