Richard is considering buying a new vehicle. Richard does not have enough to purchase outright so he will finance. He has $$9,000$ to put down and was offered dealership financing at $5\mathrm{.}2\%$ APR over $4$ years. The agreed purchase price is $$45,000.$ Tax is $7\%$ on the purchase price and title fees are $$1500,$ which are not taxed. Assume monthly compounding. Use this information to answer the following questions for Richard:

$($a$)$ What is the out the door price of Richard's new truck? $(2\mathrm{.}5$ points$)$

$($b$)$ What is Richard's monthly payment? $(2\mathrm{.}5$ points$)$

$($c$)$ What is the total interest amount paid over the loan duration? $(2\mathrm{.}5$ points$)$

Congratulations! You have two job offers on the table. Job $1$ is offering a salary of $$62,000,100\%401(k)$ matching up to $3\%,$ and historically gives $2\mathrm{.}0\%$ raises. Job $2$ is offering $$72,000,50\%401(k)$ matching up to $5\%,$ and $1\mathrm{.}75\%$ year$-$on$-$year raises. Other than salary and retirement contributions, you deem the two offers to be identical. Assume $7\mathrm{.}25\%$ yearly returns and yearly retirement contributions at the beginning of each year.

$($a$)$ If you plan to retire in $40$ years how much will your ending salary be for job $1?(2\mathrm{.}5$ points$)$

$($b$)$ If you plan to retire in $40$ years how much will your ending salary be for job $2?(2\mathrm{.}5$ points$)$

$($c$)$ If you plan to retire in $40$ years and meet each employer's match how much more or less $($$$)$ will you have in retirement if you choose the job $1?(2\mathrm{.}5$ points$)$

$($d$)$ If you plan to retire in $40$ years and contribute $5\%$ how much more or less $($$$)$ will you have in retirement if you choose job $1?(2\mathrm{.}5$ points$)$