Effective Annual Rate (EAR)

Effective Annual Rate (EAR)

The Problem with APR

• The Annual Percentage Rate (APR) does not account for the impact of compounding.
• The frequency of compounding influences the future value or present value of a cash flow.

Comparing Interest Rate Quotes

• Consider these interest rate quotes:
  • 10.8% compounded annually
  • 10.5% compounded quarterly
  • 10.2% compounded monthly
  • 10% compounded daily
• Although the APR varies, the lowest APR isn't necessarily the best option when borrowing.
• The compounding rate affects the ultimate value of a cash flow.

Effective Annual Rate (EAR) Defined

• EAR is the actual rate of interest, accounting for compounding effects.
• It allows for a true comparison between different interest rate quotes.

EAR Formula

• The formula for calculating the Effective Annual Rate (EAR) is: $EAR = (1 + APR/m)^m - 1$ Where:
  • $EAR$ = Effective Annual Rate
  • $APR$ = Annual Percentage Rate
  • $m$ = Number of compounding periods per year