Use the computer to check the steps for you as you go along. There is partial credit on this problem.

A recent college graduate borrows $60000$ dollars at an (annual) interest rate of $8.25$ per cent. Anticipating steady salary increases, the buyer expects to make payments at a monthly rate of $675 (1+t / 150)$ dollars per month, where $t$ is the number of months since the loan was made.

Let $y(t)$ be the amount of money that the graduate owes $t$ months after the loan is made.
$y(0) =$ (dollars)

With $y$ representing the amount of money in dollars at time $t$ (in months) write a differential equation which models this situation.
$y' = f( t , y ) =$ .
Note: Use $y$ rather than $y(t)$ since the latter confuses the computer. Remember to check your units, but don't enter units for this equation -- the computer won't understand them.

Find an equation for the amount of money owed after $t$ months.
$y(t) =$

Next we are going to think about how many months it will take until the loan is paid off. Remember that $y(t)$ is the amount that is owed after $t$ months. The loan is paid off when $y(t)$ =

Once you have calculated how many months it will take to pay off the loan, give your answer as a decimal, ignoring the fact that in real life there would be a whole number of months. To do this, you should use a graphing calculator or use a plotter on this page to estimate the root. If you use the the xFunctions plotter, then once you have launched xFunctions, pull down the Multigaph Utility from the menu in the upper right hand corner, enter the function you got for $y$ (using $x$ as the independent variable, sorry!), choose appropriate ranges for the axes, and then eyeball a solution.

The loan will be paid off in months.

If the borrower wanted the loan to be paid off in exactly $20$ years, with the same payment plan as above, how much could be borrowed?
Borrowed amount =