Brian has purchased a new tire. In addition, he purchased a 4-year road hazard warranty on the tire. This warranty has the following characteristics:

a. The warranty pays 200(1 .25) at the moment of damage if the tire must be replaced. The factor of 0.25 represents the pro-rata decrease in the value of the tire due to usage.

b. The warranty only pays for 1 incident

c. The force of damage requiring replacement has been determined to be = 0.05 + 0.02, 0 .

d. = 0.05 is the annual continuously compounded interest rate. The cost of the warranty to Brian (warranty price (WP) is its APV plus 10% of the WP for commission to the tire dealer plus 10% of the APV for profit.

1. What is the price of the warranty if the tire cost 350 rather than 200?

2. What is the price of the warranty a. if = 0.03 + 0.01, 0; b. = 0.06 + 0.005 2 , 0.

3. How sensitive is the price of the warranty to changes in the interest rate? You may wish to compare prices at different interest rates to support your conclusion.

4. How sensitive is the price of the warranty to changes in the commission? You may wish to compare prices at different commission rates to support your conclusion.

5. It has been decided to add an additional expense to reflect the cost of paying the claim, that is, it costs something to verify the claim, speak to the customer making the claim and sending the check. Since this expense at the time the claim is paid, it is like adding an additional lump sum to the benefit amount. Modify your model to include a claim expense of $35, paid at the EOM of claim (just as the benefit is). How did this affect the price of the warranty?