APY vs APR: Understanding Compound Interest

APR (Annual Percentage Rate) represents the simple interest rate without compounding. APY (Annual Percentage Yield) accounts for the effects of compound interest, showing what you actually earn or pay over a year.

The Formulas

  • APR to APY: APY = ((1 + APR/n)^n - 1) × 100
  • APY to APR: APR = n × ((1 + APY)^(1/n) - 1) × 100

Where n = number of compounding periods per year.

Why the Difference Matters

For savings accounts, banks advertise APY because it's higher and looks better to consumers. For loans, they quote APR because it's lower, making the loan appear cheaper. Understanding both helps you compare financial products fairly.

Continuous Compounding

When n approaches infinity, the formula becomes: APY = e^r - 1, where e ≈ 2.718. This is the theoretical maximum yield from compounding.