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APR ⇄ APY Calculator

Convert between APR and APY.

How it is calculated

In APR to APY mode the tool uses APY = (1 + APR / n)ⁿ − 1, where APR is the nominal yearly rate written as a decimal in the formula (6% is 0.06 there, but you type 6 in the rate field) and n is the number of compounding periods per year (12 monthly, 4 quarterly, 365 daily). In APY to APR mode it reverses this: APR = n × ((1 + APY)^(1/n) − 1). The answer is a percentage with 4 decimals. Compounding must happen at least once a year, and the rate cannot be negative. With n = 1 the two rates are equal. The more often interest compounds, the larger the gap between them.

Worked example

A savings account quotes 6% APR, compounded monthly. Monthly rate: 6 / 12 = 0.5%, so each month multiplies the balance by 1.005. After 12 months: 1.005¹² ≈ 1.061678. Subtract 1: 6.1678% APY. A deposit of 1,000 would therefore grow to about 1,061.68 in a year.

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Common mistakes

  • Comparing a 6% APR product with a 6% APY product as if they were equal. The APY already includes compounding, so it is the higher-paying quote at the same number.
  • Entering 0.06 instead of 6. The rate field is a percentage.
  • Using the wrong number of compounding periods, for example 1 for a monthly-compounding account. This is the most common reason for a mismatch with the bank's stated APY.
  • Applying the result to a loan with fees. APY here covers interest compounding only, not fees or other charges.

Sources

About this calculator

APR (annual percentage rate) is the simple, non-compounded nominal interest rate quoted per year, while APY (annual percentage yield), also called the effective annual rate, accounts for the effect of compounding within the year. The conversion formula is APY = (1 + APR/n)ⁿ − 1, where n is the number of compounding periods per year (12 for monthly, 365 for daily, and so on); the more frequently interest compounds, the further APY pulls above APR. The reverse conversion solves the same formula for APR given a target APY and compounding frequency.

Borrowers comparing credit card, mortgage or personal loan offers use APR because lenders are legally required to quote it, while savers comparing high-yield savings accounts or CDs look at APY since banks advertise the compounded figure. Financial analysts, accountants, and anyone shopping for the best true cost of borrowing or true return on savings use this calculator to put nominal and effective rates on the same footing.

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Comments (1)

  • Editorial team

    Compounding frequency matters less than the quoted rate itself. At 5 percent, monthly compounding gives 5.1162 percent and daily compounding 5.1267 percent, a gap of only about 0.01 points, so compare accounts by converting each one to APY rather than chasing the compounding schedule. Type the rate as a percentage, such as 5. Which account or loan quote are you trying to compare?

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