Annual Percentage Yield (APY) represents the actual yearly rate of return on an investment or savings balance, accounting for the effect of interest compounding.

What is the difference between APR and APY?

APR (Annual Percentage Rate) does not account for interest compounding within the year. APY accounts for compounding, making it the superior metric for comparing deposit accounts.

Why is APY higher than the nominal rate?

APY is higher because compounding interest calculates interest on your previously earned interest, increasing your effective annual yield.

What is daily compounding?

Daily compounding applies the interest rate to the balance 365 times a year. This yields the highest effective APY for a given nominal rate.

How does compounding frequency affect APY?

The more frequent the compounding, the higher the resulting APY. For example, 6% compounded monthly is 6.17% APY, while compounded daily it is 6.18% APY.

Finance Tool

APY Calculator

Determine the true Annual Percentage Yield (APY) for a nominal interest rate compounded at different intervals (daily, monthly, quarterly, or annually).

Interactive APY Calculator Workspace

Live Solver

Nominal Interest Rate (Stated Rate) (%)

Compounding Yield Comparison

Compounded Daily Yield (365x)5.39% APYmaximum potential yield

Compounded Monthly (12x)5.378% APYstandard banking compound

Compounded Quarterly (4x)5.354% APYinvestment fund standard

Compounded Semi-Annually (2x)5.319% APYbond coupon standard

Mathematical Formula & Variables

Equation ModelAPY = (1 + r/n)^n - 1

The Annual Percentage Yield (APY) formula computes the effective annual interest rate that includes the effect of compounding over a year.

Variable Definitions

Symbol	Description
APY	Annual Percentage Yield (effective annual rate)
r	Nominal annual interest rate (stated interest rate)
n	Number of compounding periods per year

How to Use the APY Calculator

Input the stated Nominal Interest Rate (annual rate).
Select the Compounding Frequency (e.g., Daily, Monthly, Quarterly, or Semiannually).
Review the calculated APY which reflects your true yearly rate of return.

Practical Example Calculation

Scenario Context: Finding the APY for an account with a nominal rate of 5% compounded monthly.

Step 1: Identify values: r = 5% = 0.05, n = 12.

Step 2: Apply formula: APY = (1 + 0.05 / 12)^12 - 1.

Step 3: Calculate: APY = (1 + 0.004167)^12 - 1.

Step 4: Exponent: (1.004167)^12 = 1.05116.

Step 5: Subtract 1: APY = 0.05116 or 5.116%.

The true effective Annual Percentage Yield is 5.116%.

Frequently Asked Questions

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