Question

$350,000 house at 5.1% interest, 30 year loan, assume 2.00% property tax, average home insurance at $600 per year. Assume the LTV is 80%. You have $750 per month student loan, no other long term loan, your income is $70,000 per year.

A.What is the front–end ratio? What is the back-end ratio?

B. How much you can borrow (conventional loan, 28% front-end ratio)? Give your financial information, about how much house you can afford? Assume that you pay about $583 and $50 for property tax and insurance monthly.

Answer 1

A]

Loan amount = cost of house * LTV = $350,000 * 80% = $280,000

Monthly loan payment is calculated using PMT function in Excel :

rate = 5.1% / 12   (converting annual rate into monthly rate)

nper = 30*12 (30 year loan with 12 monthly payments each year)

pv = 280000 (loan amount)

PMT is calculated to be $1,520.26

Front end ratio = (monthly mortgage payment + monthly tax + monthly insurance) / monthly income

monthly income = annual income / 12 = $70,000 / 12 = $5,833.33

Monthly tax = cost of house * property tax % per year / 12

Monthly tax = $350,000 * 2% / 12 = $583.33

Monthly insurance = annual insurance / 12 = $600 / 12 = $50

Front end ratio = ($1,520.26 + $583.33 + $50) / $5,833.33

Front end ratio = 36.92%

Back end ratio = (monthly mortgage payment + monthly tax + monthly insurance + other monthly debt payments) / monthly income

Back end ratio = ($1,520.26 + $583.33 + $50 + $750) / $5,833.33

Back end ratio = 49.78%

B]

Front end ratio = (monthly mortgage payment + monthly tax + monthly insurance) / monthly income

28% = (monthly mortgage payment + $583.33 + $50) / $5,833.33

monthly mortgage payment = $1,000

Maximum monthly mortgage payment is $1,000

Maximum loan amount is calculated using PV function in Excel :

rate = 5.1% / 12   (converting annual rate into monthly rate)

nper = 30*12 (30 year loan with 12 monthly payments each year)

pmt = -1000 (Maximum monthly mortgage payment)

PV is calculated to be $184,179.10

Maximum cost of house = Maximum loan amount / LTV

Maximum cost of house = $184,179.10 / 80%

Maximum cost of house = $230,223.87