Wize University Introduction to Finance Textbook > Time Value of Money
Effective Annual Rate
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Annual Percentage Rate vs Effective Annual Rate
Annual Percentage Rate
- APR is a quoting convention where short-term interest rates (monthly, quarterly, semi-annually, etc.) are multiplied by the number of periods in a year.
- Not particularly useful because APR does not take into account compounding!
- An interest rate is “APR” when:
- A quotation is provided;
- Compounding frequency is indicated; or
- The periodicity of the interest rate is not annual and is not specified to be “effective” (e.g. “monthly” interest rate).
- Also called the nominal rate, stated rate, or quoted rate
Effective Annual Rate
- The actual interest rate that is earned or paid, computed by adjusting the APR to reflect the number of compounding periods per year.
- Effective rate increases as compounding frequency increases because interest is calculated more often.

Where:
m = number of compounding periods per year

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Example: Effective Annual Rate
APR of 10% compounded monthly is equal to what effective annual rate?
Practice: Effective Annual Rate
Steve is planning on investing his money into a new account offered by his bank. The ad for the new account stated that the account earns 5.1% APR compounded monthly. His current account pays 5% compounded daily. Which account should he choose?