Question

A woman is looking to purchase her primary home in the Cleveland Suburbs. She has enough for a 20% down payment and an income of $40,000 per year. However, her FICO Score is 660. The prime Interest Rate for 30-year Mortgages is 4.75%. She has a car payment of $400 per month and a Student Loan Payment of $200 per month. The home she finds has 70 Effective Property Tax Mills and Homeowner’s Insurance Costs $50 per month on every $100,000 of Home Value. How much can the woman pay for the home? How large of a mortgage will the bank allow her take out?

Answer 1

Annual Income =40000

Monthly Income =40000/12 = 3333.33

We have to go by 28/36 rule.

This means she shouldn't spend more than 28% of her monthly gross income on housing which includes monthly mortgage payments (interest + principal) , property tax and home insurance This is the 28 rule

The 36 rule is that the monthly debt payments including mortgage payments and other debt like student loan, car loan etc should not exceed 36% of monthly gross income.

In the given case, car loan per month =$400 and student loan per month =$200 .

The maximum monthly debt to monthly income ratio preferred by the rule is 36% .Hence 36% x 40000/12 = $ 1200

Hence maximum monthly payments relating to the house she can make is $ 600 ( $1200 -$600)

Let the mortgage value of loan be L . Then value of property = 1.25 L( since down payment is 20% Mortgage will 80%)

Rate = prime rate + spread ( since she has FICO score of only 660). Hence additional interest rate will be up to 0.5% .We'll assume as 0.5%

Hence mortgage rate = 4.75% +0,5% = 5.25%

Rate per month r = 5.75% /12 or 0.004375 , n =30 x 12 =360 ,

Hence monthly mortgage payments = L* [ r *( 1 +r)^n ] / [ (1 +r)^360 -1 ] = L* [0.004375*(1+0.004375)^360] / [ (1 + 0.004375)^360 -1 ] = 0.005522037L

Property tax = 70/1000/12 x 1.25L = 0.07 x 1.25L =0.0875/12*L, Home Insurance = 50/100000*1.25L =0.000625L

We know Mortgage payments = Max . Monthly housing payments - Property tax monthly -Home insurance monthly

Therefore 0.005522037L = 600 - (0.0875/12)L - 0.000625L

Therefore 0.0134387 L = 600 , Hence L = $ 44647

Hence the Mortgage amount will be $ 44647

Down payment by the woman will be $ 44647/0.8 x 0.2 =$ 11162

Hence the maximum loan amount will be $ 178920   =PV(4.75%/12,360,-933.33,0)

178920/0.8 =223,650 is value of home , Down payment = 44,730