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Lecture 5 (2) - Chapter 6 Effective Interest Rates and Loan...

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Chapter 6 Effective Interest Rates and Loan Types
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Annual Percentage Rate vs Effective Annual Rate What is the difference between an Annual Percentage Rate (APR) and an Effective Annual Rate (EAR)? The APR is the interest rate that is quoted to you, but the EAR is the interest rate you’re really paying. The relationship between the APR and the EAR will depend on how many times interest is calculated per year. This concept is called the compounding period. Whenever the interest is compounded more than once per year the EAR > APR.
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What exactly are we doing? To find the effective annual interest rate when interest is compounded more than once per year we use the formula: (1 + EAR) = (1 + APR/m) m EAR = (1 + APR/m) m -1 Essentially what this formula tells us to do is take the rate we’re quoted divided by the number of times interest is compounded per year. So we see that (1+ APR/m) = the m thly interest rate. Then we raise it to the m th power and subtract 1 to get the EAR.
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Example 1 Suppose you need a loan to buy a car. Bank A offers you the loan at a 12% annual interest rate. Bank B offers you the loan at 11.75% compounded semiannually (twice a year). Bank C will lend you the money at 11.65% compounded quarterly (four times a year), Bank D will charge you 11.5% compounded monthly and Bank E charges 11.4% compounded daily. Which bank should you choose to borrow from? The formula to find an effective interest rate from the quoted annual rate is: EAR = (1 + APR/m) m -1 Bank A charges you (1 + 0.12/1) 1 -1 = 0.12 = 12% Bank B charges you (1 + 0.1175/2) 2 – 1 = 0.1210 = 12.10% Bank C charges you (1 + 0.1165/4) 4 – 1 = 0.1217 = 12.17% Bank D charges you (1 + 0.11.5/12) 12 – 1 = 0.1213 = 12.13% Bank E charges you (1 + 0.11.4/365) 365 – 1 = 0.1207 = 12.07%
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Example 2 You want to buy a TV for $500. You have three credit cards that you can use. Your Discover card charges you 15% compounded daily.
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