Chapter 1.1, Problem 17E

Round all answers to two decimal places unless otherwise indicated.

Note Some of the formulas below use the special number $e$, which was presented in the Prologue.

17. How Much Can I Borrow? The function in Example 1.2 can be rearranged to show the amount of money $P=P\left(M,r,t\right)$ in dollars, that you can afford to borrow at a monthly interest rate of r (as a decimal) if you are able to make t monthly payments of M dollars:

$P=M\times \frac{1}{r}\times \left(1-\frac{1}{{\left(1+r\right)}^t}\right)$

Suppose you can afford to pay $350 per month for 4 years.

a. How much money can you afford to borrow for the purchase of a car if the prevailing monthly interest rate is 0.75%? (That is a 9% APR.) Express the answer in functional notation, and then calculate it.

b. Suppose your car dealer can arrange a special monthly interest rate of 0.25% (or a 3% APR). How much can you afford to borrow now?

c. Even at a 3% APR, you find yourself looking at a car you can't afford, and you consider extending the period during which you are willing to make payments to 5 years. How much can you afford to borrow under these conditions?