Question $4$:

A $20-$unit apartment building is for sale. Lisa wants to buy it and needs to arrange a mortgage of $3,000,000$ at j$^2=8\%$ amortized over $25$ years with monthly payments. The banker assessed the lending value of the property to be $4,000,000.$ The banker requires a minimum DCR of $1\mathrm{.}15.$ The fair market rent would be $2,000/$unit per month. Operating expenses for the building are $200,000$ per year and property taxes are $10,000$ a year.

$($a$)$ Does Lisa qualify for the loan?

$($b$)$ What is the maximum size of loan supported by the incomes of the building?

$($c$)$ Suppose the banker only wants to lend a maximum of $80\%$ of the lending value of the building. Given $($b$)$ and this restriction, what is the size of loan Lisa can actually get?