Answer:
The amount of the most expensive house Jim can buy is $1,329,720.81.
Explanation:
Maximum LTV = 80%.
Annual income = $240,000
Monthly total income = Annual income / 12 = $240,000 / 12 = $20,000
Maximum front end DTI limit = 28%.
Front end DTI = (Monthly mortgage payment using Front end DTI + Monthly tax + Monthly insurance) / Monthly total income
28% = (monthly mortgage payment using Front end DTI + $140 + $70) / $20,000
28% * $20,000 = Monthly mortgage payment using Front end DTI + $210
$5,600 = Monthly mortgage payment using Front end DTI + $210
Monthly mortgage payment using Front end DTI = $5,600 - $210 = $5,390
Maximum back end DTI is 36%.
Back end DTI = (monthly mortgage payment using Back end DTI + monthly tax + monthly insurance + other debt payments) / monthly gross income.
36% = (monthly mortgage payment using Back end DTI + $140 + $70 + $178) / $20,000
36% * $20,000 = Monthly mortgage payment using Back end DTI + $388
$7,200 = Monthly mortgage payment using Back end DTI + $388
Monthly mortgage payment using Back end DTI = $7,200 - $388 = $6,812
Maximum monthly mortgage payment to satisfy both Front and Back end DTI = Lower of Monthly mortgage payment using Front end DTI and Monthly mortgage payment using Back end DTI = Monthly mortgage payment using Front end DTI = $5,390
The loan amount can now be calculated using the following Excel PV function:
Loan amount = PV(rate,nper,-pmt) .............................. (1)
Where:
rate = Monthly rate = Annual rate / 12 = 4.5% / 12 = 0.045 / 12 = 0.00375
nper = Number of period or months = Numbers of years of loan tenure * 12 = 30 * 12 = 360
pmt = monthly payment = Maximum monthly mortgage payment to satisfy both Front and Back end DTI = $5,390
Substituting all the values into equation (1), we have:
Maximum loan amount = PV(0.00375,360,-5390) ................. (2)
Inserting =PV(0.00375,360,-5390) in any cell in an Excel sheet, we have:
Maximum loan amount = $1,063,776.65
Maximum house value can be calculated using the following formula:
LTV = Maximum loan amount / Maximum house value ……..……….. (3)
Substituting the relevant values into equation (2), we have:
80% = $1,063,776.65 / Maximum house value
Maximum value of house = $1,063,776.65 / 80%
Maximum value of house = $1,329,720.81
Since the Maximum value of house is $1,329,720.81, this implies that the amount of the most expensive house Jim can buy is $1,329,720.81.
