Question

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.

Answer 1

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) *[(1-(1)/((1+r)^(N) ) )/(r) ] \\\\ PV = 1200 *[(1-(1)/((1+0.00416667)^(360) ) )/(0.00416667) ] \\\\ PV = 1200 *[(1-(1)/((1.00416667)^(360) ) )/(0.00416667) ] \\\\ PV = 1200 *[(1-(1)/(4.467744319 ) )/(0.00416667) ] \\\\ PV = 1200 *[(1-0.223826595 )/(0.00416667) ] \\\\ PV = 1200 *[(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.