© M. Spiegel and R. Stanton, 2000 Auto Loan Banks

Overview of Lecture 4

s Examples of Quoted vs. True Interest Rates

? Banks ? Auto Loan

s Forward rates, spot rates and bond prices

? How do things change when interest rates vary over different periods?

? Present Value in terms of spot/forward rates ? Converting between forward and spot rates ? Calculating forward/spot rates from bond prices (what information

can we get out of bond prices?)

? M. Spiegel and R. Stanton, 2000

1

U.C. Berkeley

Bank Interest Calculations

s The sign in the window reads:

? Interest rate: 8% compounded daily. ? Effective annual yield: 8.33%.

s What do these numbers mean? s Which (if either) is a true annual interest rate?

? What amount will you actually earn in 1 year per dollar invested?

? M. Spiegel and R. Stanton, 2000

2

U.C. Berkeley

Bank Interest Calculations

s "Compounded daily": Each day the bank

multiplies the prior day's balance by (1 + .08/365)

? True daily interest rate = .08/365 = 0.022%

s Over 1 year your earnings per dollar are

[ ] 1+

.08 365

365

= 1.0833.

s Quoted rate of 8% (APR) is not a true interest rate s Effective annual yield, 8.33%, is a true interest rate.

? M. Spiegel and R. Stanton, 2000

3

U.C. Berkeley

An Actual Auto Loan

s The advertisement says: "12 month car loans. Only 9%!"

s The small print shows the payments are calculated on a $10,000 car as follows:

? On a 12 month $10,000 loan with 9% interest rate, you owe a total of $10,900.

? Twelve equal payments come out to 10,900/12 = 908.33 per month.

s Is 9% the actual interest rate on the loan?

? M. Spiegel and R. Stanton, 2000

4

U.C. Berkeley

Auto Loan Calculating the True Interest Rate

s The true interest rate must set the present value of the payments equal to the initial loan.

( ) ( ) 10,000

=

908.33 1+ rmonthly

+

908.33 1+ rmonthly

2

+ ... +

908.33 1+rmonthly 12

s Therefore rmonthly = 1.35%

s The annual interest rate rannual = (1+rmonthly)12-1 = 17.5% percent per year!

? M. Spiegel and R. Stanton, 2000

5

U.C. Berkeley

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