APY Calculator: Convert APR, APY and Balance Growth

APY calculator

Convert a nominal annual rate to APY, convert APY to an equivalent nominal rate, or find the annualized yield from two balances.







APY formulas

For a nominal annual rate r compounded n times per year, APY = (1 + r ÷ n)n − 1. For continuous compounding, APY = er − 1.

To convert APY back to an equivalent nominal rate, r = n × ((1 + APY)1/n − 1). With continuous compounding, r = ln(1 + APY).

When starting balance P, ending balance A and period t in years are known, APY = (A ÷ P)1/t − 1. This assumes there were no deposits or withdrawals during the period.

Examples

  • A 5% nominal rate compounded monthly has an APY of about 5.116%.
  • A 5% APY is equivalent to about 4.889% nominal APR with monthly compounding.
  • A balance growing from $10,000 to $10,500 in 12 months has a 5% APY.
  • A balance growing 2% in six months has an annualized APY of about 4.04%.

APY versus APR

APY includes the effect of compounding and is useful for comparing deposit yields. A nominal APR states the annual rate before intra-year compounding. When compounding occurs more than once per year and the rate is positive, APY is higher than the nominal APR.

Limits and assumptions

The projection assumes a constant rate, a fixed compounding convention and no deposits, withdrawals, taxes, fees or penalties. The balance-based mode treats all growth as yield. It is not appropriate when cash flows occurred during the measurement period. Institutions can use different posting and day-count rules.

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