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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.

%

Optionally calculate the future value with interest:

$
years
Annual Percentage Yield (APY)
4.8547881%
Nominal Rate (APR)
4.75%
APY
4.8547881%
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%

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

What is APY?

Annual Percentage Yield (APY) is the effective annual rate of return when compounding is taken into account. It represents the actual amount of interest earned on a deposit over one year, including compound interest.

What is the difference between APR and APY?

APR (Annual Percentage Rate) is the nominal interest rate without compounding. APY includes the effect of compounding. APY is always equal to or higher than APR. For example, 5% APR compounded monthly produces an APY of 5.116%.

How is APY calculated?

APY = (1 + r/n)^n - 1, where r is the nominal annual rate (as a decimal) and n is the number of compounding periods per year. For continuous compounding, APY = e^r - 1.

Does compounding frequency matter?

Yes. More frequent compounding produces a higher APY from the same nominal rate. The difference is more significant at higher interest rates. At 5% APR, the difference between annual and daily compounding is about 0.13 percentage points.

Why do banks advertise APY?

Banks advertise APY for savings accounts and CDs because it reflects the true return a depositor receives. For loans, banks typically show APR instead, which appears lower. Regulations like the Truth in Savings Act require banks to disclose APY.

What is continuous compounding?

Continuous compounding is the theoretical limit of compounding frequency — interest is calculated and reinvested at every instant. The formula uses Euler's number: FV = PV × e^(r×t). In practice, daily compounding is nearly identical.