Q:

# Randy can afford a \$1200 monthly mortgage payment. If the current mortgage rates are 5% and he wishes to have a 30-year mortgage, what is the maximum amount he can afford to borrow?Show your work.

Accepted Solution

A:
Given is amount of Monthly payments, Pm = 1,200 dollars. Given is Rate of interest at 5% i.e. r = 0.05/12 = 0.00416667. Given is the Time period of 30-years loan i.e. N = 30 x 12 = 360. It says to find Present Value of loan amount, PV = ? Using the Mortgage Formula for Present value of loan when Pm, r, N is given $$PV = P_{m} *[\frac{1-\frac{1}{(1+r)^{N} } }{r} ] \\\\ PV = 1200 *[\frac{1-\frac{1}{(1+0.00416667)^{360} } }{0.00416667} ] \\\\ PV = 1200 *[\frac{1-\frac{1}{(1.00416667)^{360} } }{0.00416667} ] \\\\ PV = 1200 *[\frac{1-\frac{1}{4.467744319 } }{0.00416667} ] \\\\ PV = 1200 *[\frac{1-0.223826595 }{0.00416667} ] \\\\ PV = 1200 *[\frac{0.776173404}{0.00416667} ] \\\\ PV = 1200 * 186.2814681 \\\\ PV = 223,537.7617 \approx 223,537.76 \;dollars.$$Hence, he can afford to borrow a maximum of 223,537.76 dollars.