The balance stays the same as we would expect.

Here are some other checks that you should try. What happens if we don't pay anything every month? What about if we pay $2000 every month, how long does it take to pay the loan at $2000 per month?

Click here for answer.

This is our first example of a root search problem. Normally, Mathematica is very good
at solving such problems using its FindRoot function. But the special nature of the balance function, which is a recursive function defined only for an integer number of months, makes this problem somewhat harder. We will address this question in greater detail later in the course.

Instead, let's solve it graphically. Start by making a table of the balance on the loan for 75 months, and then plot it using the ListPlot command.

That is

bal=Table[balance[i, 2000, .07/12],{i, 0, 75}];

ListPlot[bal];

We see that the graph crosses zero right at about 60 months, so at $2000 per month it takes almost exactly five years to pay off the loan. Making a big table like this is somewhat inconvenient, if we make the payment just a little over the ``break even'' amount of
$583.33 the table would have to be very large.