Here is a multipart example on finance. Be patient and
careful as you work on this problem. You will probably be surprised
to find how long it takes to get all of the details of solution of a
realistic problem right, even when you know how to do each of the
steps. 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 dollars at an (annual) interest
rate of per cent. Anticipating steady salary increases, the buyer
expects to make payments at a monthly rate of dollars per
month, where is the number of months since the loan was made.
Let be the amount of money that the graduate owes months
after the loan is made.
(dollars)
With representing the amount of money in dollars at time (in months) write a
differential equation which models this situation.
.
Note: Use rather than since the latter confuses the computer.
Don't enter units for this equation.
Find an equation for the amount of money owed after months.
(dollars)
Next we are going to think about how many months it will take until
the loan is paid off. Remember that is the amount that is
owed after months. The loan is paid off when
=
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 (using 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 years, with
the same payment plan as above, how much could be borrowed?
Borrowed amount =
You can earn partial credit on this problem.