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APY Calculator

Calculate annual percentage yield from a nominal interest rate and compounding frequency. Optionally estimate future value and total interest.

APY Worksheet
%

Optionally calculate the future value with interest:

$
Annual percentage yield 4.8547881%
Nominal rate (APR)4.75%
APY4.8547881%
Formula: APY = (1 + r/n)^n - 1
APY Comparison by Compounding Frequency
CompoundingAPY at 5%APY at 10%
Annually5.000%10.000%
Semi-annually5.063%10.250%
Quarterly5.095%10.381%
Monthly5.116%10.471%
Daily5.127%10.516%
Continuously5.127%10.517%

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APY Formula

Annual Percentage Yield accounts for compound interest:

APY = (1 + r/n)n - 1

Where r is the nominal annual interest rate (as a decimal) and n is the number of compounding periods per year.

For continuous compounding:

APY = er - 1

APR vs. APY

FeatureAPRAPY
Full nameAnnual Percentage RateAnnual Percentage Yield
CompoundingNot includedIncluded
ValueLower or equalHigher or equal
Used forLoans, credit cardsSavings, CDs
RegulationTruth in Lending ActTruth in Savings Act

Effect of Compounding Frequency

Higher compounding frequency increases APY, but with diminishing returns. The table below shows APY for a 6% nominal rate:

FrequencyPeriods (n)APY
Annually16.000%
Semi-annually26.090%
Quarterly46.136%
Monthly126.168%
Daily3656.183%
Continuously∞6.184%

Future Value with Compound Interest

If you deposit a lump sum, the future value after t years is:

FV = PV × (1 + r/n)n×t

Where PV is the initial deposit, r is the nominal rate, n is compounding periods per year, and t is the number of years.

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Frequently Asked Questions

How do you calculate APY with monthly compounding?

APY = (1 + r/12)^12 - 1, where r is the annual rate as a decimal. A CD paying 4.8 percent compounded monthly has an APY of (1.004)^12 - 1, about 4.907 percent. On a $10,000 deposit held one year that earns $490.70, not the $480 the nominal rate implies.

What is the difference between APR and APY?

APY includes compounding and APR does not, so APY is always equal to or higher than APR. A 5 percent APR compounded monthly gives an APY of 5.116 percent. Banks quote APY on savings and CDs because it looks higher, and APR on loans because it looks lower. Compare APY to APY only.

What is APY?

Annual Percentage Yield (APY) is the effective annual return on a deposit once compound interest is counted. It is the actual percentage a balance grows in one year, including interest earned on interest. In the United States the Truth in Savings Act requires banks to disclose APY on deposit accounts.

Does daily compounding give a higher APY than monthly?

Yes, but only slightly. More frequent compounding raises APY, and the gap grows at higher rates. At 5 percent, the difference between annual and daily compounding is about 0.13 percentage points, and daily versus monthly is about 0.01 points. Continuous compounding, APY = e^r - 1, is the upper limit.