APY Calculator

Turn a nominal APR into its effective annual yield (APY) using APY = (1 + r/n)^n - 1, then see the interest and final balance on your deposit.

Quick Facts

Formula
APY = (1 + r/n)^n - 1
r is the APR as a decimal, n is compounding periods per year. Continuous compounding uses APY = e^r - 1.
Why it matters
APY reflects compounding; APR does not
APY is the standard, comparable figure for savings accounts and CDs.

Your Results

Calculated
Effective APY
-
Annual percentage yield
Final balance
-
Principal plus interest
Interest earned
-
Over the full term
APY minus APR
-
Boost from compounding

Ready

Enter an APR, pick a compounding frequency, and calculate.

What this calculator does

This tool converts a nominal annual interest rate (APR) into an annual percentage yield (APY), the effective rate you actually earn once compounding is taken into account. Enter the stated rate, choose how often interest compounds, and the calculator returns the APY along with the interest earned and final balance on your deposit over the term you specify.

The formula

APY is defined by the standard compounding formula:

  • APY = (1 + r/n)n - 1, where r is the nominal annual rate as a decimal (5% = 0.05) and n is the number of compounding periods per year.
  • Continuous compounding is the limit as n grows without bound: APY = er - 1.
  • The final balance follows from the yield: balance = principal x (1 + APY)t for a term of t years, and interest earned is the balance minus the principal.

This assumes a fixed rate for the whole term with no additional deposits or withdrawals. For a 5% APR compounded monthly, r/n = 0.05/12 and n = 12, giving APY = (1 + 0.05/12)12 - 1 = 5.116%.

Interpreting the output

APY is the number to compare across accounts, because it already folds in compounding while APR does not. Two accounts can advertise the same APR but pay different amounts if one compounds daily and the other annually. The "APY minus APR" figure shows exactly how much the compounding frequency adds. Notice how quickly it plateaus: moving from annual to monthly compounding matters far more than moving from daily to continuous.

Things to check

  • Enter the rate as a percent (5 for 5%), not a decimal.
  • Confirm the compounding frequency matches the account's disclosure — most US savings accounts and CDs compound daily or monthly.
  • The deposit and term only convert the yield into dollars; they never change the APY itself.

Frequently Asked Questions

What is the difference between APR and APY?
APR is the nominal (stated) annual rate and ignores compounding. APY is the effective annual yield after compounding: APY = (1 + r/n)^n - 1, where r is the APR as a decimal and n is the number of compounding periods per year. A 5% APR compounded monthly works out to about 5.12% APY, which is why APY is the right number for comparing accounts.
How is APY calculated?
Divide the nominal annual rate by the number of compounding periods per year, add 1, raise the result to the power n, then subtract 1: APY = (1 + r/n)^n - 1. For daily compounding n is 365; for continuous compounding the formula becomes APY = e^r - 1.
Does compounding more often always increase APY?
Yes, but with rapidly diminishing returns. At a 5% APR, annual compounding yields exactly 5%, monthly about 5.116%, daily about 5.127%, and continuous compounding only slightly more than daily. Beyond monthly compounding, the frequency matters far less than the rate itself.
Does the deposit amount change the APY?
No. APY depends only on the nominal rate and the compounding frequency. The deposit and time inputs simply translate the yield into dollars: final balance = deposit x (1 + APY)^years, assuming a constant rate with no deposits or withdrawals during the term.

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