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. $2If$ 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 $is.3If$ 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, $soit$ 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 $is9\%$ per year, which car should you purchase? Show all

calculations and explain carefully.