Project $1$ for Mathematical Modeling

Question $1$: $20$ points

With the rising price of gas, you wish to buy a new $($hybrid$)$ car this year. You narrow your choices to the following hyprids, $2018$ Toyota Prius, $2018$ Ford Fusion, $2018$Toyota Camry, $2018$ Hyundai Sonata, $2018$ Kia Optima. Each company has offered you its "best deal" as listed below. You are able allocate approximately $$450$ for a car payment each month for up to $60$ months. Use a dynamical system to determine which of

the new hybrid cars you could buy.

a$)$ Model this situation on an excel spreadsheet. Make sure the spreadsheet shows a month

by month breakdown of interest paid, amount owed and if and when the car will be paid

off in the required $60$ month time frame.

b$)$ Write a paragraph to describe which car you will purchase and why?

c$)$ Extra Credit: Show how putting this money into savings and paying cash for the car is

actually better than all other options!

Question $2$: $20$ points

You are considering a $30-$year mortgage that charges $0\mathrm{.}4\%$ interest each month to pay off

a $$250,000$ mortgage.

a$.$ Determine the monthly payment p that allows the loan to be paid off in $360$ months.

$($please use Excel to guess and test with your equations you've created trying with

different payments p$,$ until you get within $$10$ for last payment $-$ this is not an

exercise to solve using logarithms, etc.$)$

b$.$ Now assume that you have been paying the mortgage with payment p for $8$ years and

now have an opportunity to refinance the loan. You have a choice between a $20-$year

loan at $4\%$ per year with interest charged monthly and a $15-$year loan at $3\mathrm{.}8\%$ per year

with interest charged monthly. Each of the loans charges a closing cost of $$2500.$

Determine the monthly payment p for both the $20-$year load and the $15-$year loan. Do

you think refinancing is the right thing to do$?$ If so$,$ do you prefer the $20-$year or the

$15-$year option?