APY Calculator

The calculator converts a nominal annual rate into the yield you earn over a full year once compounding is counted:

APY = (1 + rate ÷ n)^n − 1, where n is 365, 12, 4 or 1 for daily, monthly, quarterly or annual compounding.

With the defaults (5%, monthly) the APY is 5.12% and the difference versus the nominal rate is 0.12 percentage points. On $10,000 left for a year, that is about $511.62 of interest rather than $500.

Both figures are shown to two decimals, which hides small differences at low rates. At 0.5% compounded daily, the exact APY is 0.5012%, so the difference row reads 0.00%. With annual compounding the APY always equals the rate; the difference row may then show -0.00%, which is a rounding artefact and means zero.

Two things stand out. The jump from annual to quarterly matters more than the step from monthly to daily, which is about 0.01 points at these rates. And daily compounding is already close to the mathematical ceiling: at 5%, daily gives 5.1267%, while compounding continuously would give only 5.1271%. Any account advertising "more frequent" compounding than daily is offering a difference too small to see in the result.

Banks usually headline the APY. If you need the nominal rate instead, for example to enter it in a calculator that asks for the rate and compounding separately, reverse the formula:

rate = n × ((1 + APY)^(1/n) − 1)

A 4.50% APY compounded monthly comes from a rate of about 4.41%; compounded daily, about 4.40%. To check, enter 4.41% with monthly compounding here: the result is 4.50%.

The calculator always measures a full year. For a deposit that runs for a set number of days, Regulation DD (Truth in Savings) uses APY = 100 × ((1 + interest ÷ principal)^(365 ÷ days) − 1). A 182-day CD that pays $200 on $10,000 has an APY of about 4.05%, a little more than the 4% you would get by doubling the half-year return.

The same arithmetic shows the effective yearly cost of debt that compounds. If a card charges 24% a year and compounds daily, enter 24% with daily compounding: an unpaid balance grows by about 27.11% in a year. With monthly compounding the figure is 26.82%. Treat it as a way to see what the stated rate becomes if interest is left to build up, not as a figure your card statement will show.