How to calculate APY from a nominal rate
Enter the quoted rate in Nominal (stated) annual rate (%) and choose Compounding frequency. APY Calculator then shows the effective annual yield, formula, and selected assumptions. Add Deposit amount ($, optional) and Time held (years, optional) when you also want a projected balance.
- Enter the percentage in Nominal (stated) annual rate (%).
- Choose Compounding frequency, such as Monthly (12/year) or Continuous.
- Enter Deposit amount ($, optional) for a balance projection.
- Enter Time held (years, optional), or leave it blank to use 1 year.
- Click Calculate and read the APY, formula, and assumptions.
- Click Copy result, Download result (.txt), or Reset.
APY formula for each compounding choice
Annually, Semi-annually, Quarterly, Monthly, Bi-weekly, Weekly, and Daily use APY = (1 + r/n)^n - 1. In that formula, r is the nominal rate as a decimal and n is the number of compounding periods per year. Continuous uses APY = e^r - 1.
With the values below, APY Calculator reports 5.1162%:
Nominal (stated) annual rate (%): 5
Compounding frequency: Monthly (12/year)
Deposit amount ($, optional): 10000
Time held (years, optional): 1
Effective annual yield (APY): 5.1162%
Ending balance after 1.00 yr: $10,511.62
Interest earned: $511.62How the balance projection uses APY
APY depends on Nominal (stated) annual rate (%) and Compounding frequency. When Deposit amount ($, optional) is greater than zero, APY Calculator applies Principal x (1 + APY)^Years. A blank or zero deposit leaves Ending balance and Interest earned out of the result. A blank Time held (years, optional) uses 1 year, while an entered value can include part of a year.
What APY Calculator validates
Nominal (stated) annual rate (%) accepts values from 0 through 100. Deposit amount ($, optional) accepts 0 or greater. An entered Time held (years, optional) must be above 0 and no more than 100 years. Invalid input hides the result and displays an error.
The calculation holds the rate and frequency constant. It has no fields for fees, taxes, withdrawals, deposits during the period, tiered rates, or rate changes. APY Calculator uses the values you enter and does not fetch live rates, bank records, or account data.
What to compare with APY
Compare quoted rates after matching their compounding choices. For a savings estimate, enter a deposit and holding period to see the projected balance and interest earned.
Monthly (12/year), Daily (365/year), and Continuous show how frequency changes the result for one nominal rate. Copy the displayed formula and assumptions into a calculation note when you need to retain the inputs.
When to use APY Calculator or another calculator
Use APY Calculator for an effective annual yield based on a nominal rate and compounding frequency. Choose APR Calculator for a loan APR that includes fees, term, payment frequency, and payment timing. Choose Amortization Calculator for a period-by-period loan balance, principal, and interest schedule. For growth with principal, contributions, fees, and a term, use Compound Interest Calculator. Browse Financial Calculators for the category.
Frequently asked questions
How do I calculate APY from a nominal rate?
Enter the nominal rate and choose Compounding frequency, then click Calculate. APY Calculator applies (1 + r/n)^n - 1, or e^r - 1 for Continuous.
What is the APY formula for monthly compounding?
Monthly compounding uses APY = (1 + r/12)^12 - 1, with the nominal annual rate converted to a decimal before calculation.
Can APY Calculator show interest on a deposit?
Yes. Enter a positive Deposit amount ($, optional) and Time held (years, optional) to see an ending balance and interest earned alongside APY.
What does APY Calculator reject?
It rejects a missing or out-of-range nominal rate, a negative deposit, and entered time held that is 0 or less or above 100 years. The result stays hidden until the inputs pass validation.
Does APY Calculator use live bank rates?
No. It calculates from the values you enter and does not fetch live rates, bank records, or account data.