You are going to purchase a new car, but being a responsible consumer means doing a little bit of research...

You are going to purchase a new car, but being a responsible consumer means doing a little bit of research first.

First, you find the vehicle you are purchasing and its price.
Vehicle: Chevy Volt
Price: $39,145

Current interest rate: 3%

1. Using the function A(t)=P(1+

   r

   n

   )nt, create the function that represents your new car loan that is compounded monthly. The principle will be the price of the vehicle you selected, not how much you are putting down.
2. Being a smart financial planner, you want to figure out how many months it will be until your principal is paid down to $10,000.00. Solve for t and show all of your work. Note that t will be negative because the number of months will decrease the principal.
3. Lastly, you decide to keep track of your loan four times a month instead of monthly. Solve for the adjusted interest rate.