Show all work. Label and clearly explain your answer. This is very important. $1)$ You must explain how you arrived at your

answer in order to get full credit. $2)$ If you do show your work, and your answer is wrong, you can still earn a substantial

amount of credit depending on how serious the error is$.3)$ If your answer is wrong, and you don't show your work, you will

get a zero.

Forty years ago, a gallon of gas cost $$1\mathrm{.}20.$ Today, a gallon of gas costs $2\mathrm{.}60.$

Suppose that the gas price increase has been entirely due to inflation.

a$.$ Calculate the annual inflation rate.

b$.$ Today, you plan to make a cash purchase for a new car. The Model K costs $$24,000$

and you estimate the car will last $10$ years and require $600$ gallons per year. The

Model M costs $$28,000$ but gets better mileage, so it will only require $400$ gallons per

year. The cars are identical in all other respects, and they will both be worthless after

$10$ years.

Assume that gas prices will rise by the rate of inflation $($that you calculated in part a$).$

Further assume that all gas expenditures are incurred at the end of the year. If the

nominal interest rate is $9\%$ per year, which car should you purchase? Show all

calculations and explain carefully.