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APY Calculator

Calculate Annual Percentage Yield APY and Effective Annual Rate EAR

Nominal APR (%)
Compounding

APY Formula

APY/EAR = (1 + r/n)^n - 1 (discrete)
APY/EAR = e^r - 1 (continuous)
r = nominal rate, n = compounds/year

APY is the standard measure of actual annual investment return.

⚠ The difference between APR and APY is compounding. Always compare APY when evaluating different products.

What Is APY?

APY (Annual Percentage Yield) is the real annual rate including compounding effects, also known as EAR (Effective Annual Rate). It reflects the true annual return and is the standard for fair comparison between financial products.

APR vs APY

APR = nominal (no compounding), APY = actual (with compounding). APY ≥ APR.

Frequency Impact

Higher frequency = higher APY. Daily ≈ 12.75%, monthly ≈ 12.68%, annual = 12% (for 12% APR).

Continuous

e^r-1 is the continuous compounding APY. e≈2.71828 is the theoretical limit.

Applications

Bank deposits, money market funds, bonds, and investment products all use APY.

Teaching Example: APR=12%, monthly (n=12). Monthly rate=12%/12=1%. APY=(1+0.12/12)^12-1=(1.01)^12-1=12.68%. So 12% nominal monthly = 12.68% actual. Daily would give 12.75%.

Applications

Bank Deposits Investment Products Bond Investing Loan Comparison Investment Analysis

Frequently Asked Questions

Nominal APR vs EAR?▼
APR is stated without compounding. EAR/APY includes compounding. 12% APR monthly = 12.68% EAR.
APY vs APR?▼
APR = nominal without compounding. APY = actual yield including compounding. Use APY for fair comparison.
What is continuous compounding?▼
Infinite compounding frequency. EAR=e^r-1. 12% continuous = 12.75%, slightly above monthly (12.68%).
Why use APY instead of APR?▼
Different compounding frequencies make APR incomparable. APY unifies them on an annual scale including compounding.

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