Richard is considering buying a new vehicle. He has the option to purchase a $2024$ Chevrolet Colorado $271($with $4-$wheel drive of course$).$ Richard does not have enough to purchase outright so he will finance. He has $$5,000$ to put down and was offered dealership financing at $4\mathrm{.}9\%$ APR over $3$ years. The agreed purchase price is $$43,000.$ Tax is $7\%$ on the purchase price and title fees are $$1200,$ which are not taxed. Assume monthly compounding. Use this information to answer the following questions for Richard: can you answer this on excel and show formulas please

$($a$)$ What is the out the door price of Richard's new truck?

$($b$)$ What is Richard's monthly payment?

$($c$)$ What is the total interest amount paid over the loan duration?

$($d$)$ Upon hearing his monthly payment, Richard starts to get cold feet. The car salesman informs Richard that he can get the same rate on a $5$ year loan, which is rare, and therefore a great deal for Richard. Richard questions the longer duration, but the salesman tells Richard this will not matter since "the rate is the same." How much additional total interest will Richard pay if he chooses the $5$ year loan term over the $3$ year term?