Case $3$: maximum monthly payment only

If the user has not provided the square footage but has provided the maximum monthly payment,

calculate the maximum square footage that their monthly payment can afford in the location specified.

You will need to account for the amount of tax owed per month in determining how big a house the

monthly payment allows for. While there is an algebraic solution for this problem, it gets a bit messy

and because of numerical errors$/$precision can sometimes provide not accurate results. Instead, we

recommend that you estimate the maximum square footage that the individual can afford using an

approximation method. To do this, follow the algorithm shown below.

$$ Start with an initial estimate for the maximum square footage $($e$.$g$.100$ ft$2$

$)$

$$ While the maximum square footage has not been found:

o Calculate the estimated home cost, the principal loan amount, the monthly payment

towards the loan, and the monthly payment for the annual taxes.

o If the two monthly payments sum to a value greater than the maximum monthly payment

provided by the user, reduce the maximum square footage by $1$ ft$2$ and exit the loop;

otherwise, increase the maximum square footage by $1$ ft$2$

$.$

$$ Calculate the final monthly payments based on the maximum square footage estimated and

report this value to the user.

Report the max monthly payment as shown below. In the starter code, we provide an incomplete string

that you need to fill with the correct formatting for numbers using the example message below $($in red$).$

In East Lansing, a maximum monthly payment of $$3,200\mathrm{.}00$ allows the purchase of a house of $2,708$ sq$.$ feet for $$460,360$

assuming a $30-$year fixed rate mortgage with a $$60,000$ down payment at $6\mathrm{.}7\%$ APR.