Question

Big Bank will make Duane Miller a mortgage loan if it meets the 28/36 rule. His annual gross income is $45,000. He has a $675 monthly auto payment and the property taxes & homeowners insurance for a new home will cost $3,000 annually. Big Bank will give him a 30-year mortgage with a 7.5 percent fixed rate. Duane will make a 20% down payment.

1. What maximum purchase price for a home can Duane afford (how much house can he buy)? Round your answer to the nearest $1,000 and show your work.

2. Assume Duane pays off his auto loan thereby eliminating the $675 monthly payment. What maximum purchase price for a home can Duane now afford? Round your answer to the nearest $1,000 and show your work.

Answer 1

As per 28/36 rule, an individual can spend a mximum of 28% of his gross income on his housing debt including housing expenses. And a maximum of 36% of his gross income on total debt which includes housing, car and other debt services.

Annual Gross income = $45,000

Annual Auto payment =$675 per month*12

= $8100

Property taxes & homeowners insurance = $3000 annually

Down-payment = 20%

a). Calculating the maximum purchase price for a home can Duane afford:-

Since, Duane is paying auto debt payments he will be covered in 36% rule.

Maximum debt service amount = Annual Gross income*36%

=$45,000*36%

= $16200

Debt payment available for housing loan = $16200 - $8100 - $3000

= $5100

Monthly home loan payment = $ 5100/12

= $425

Using, the monthly payment to calculate the Home loan amount:-

where, P = loan amount

r = Periodic Interest rate =7.5%/12 = 0.625%

n= no of periods =30yrs*12 = 360

EMI = monthly payment = $425

P = $ 60782.49

Loan amount = $ 60782.49

Down-payment = 20%

Maximum purchase price of home = Loan amount/(1-Down-payment)

= $60782.49/(1-0.20)

= $ 75,978.11

So, maximum purchase price for a home can Duane afford is $ 75,978.11

b). Calculating the maximum purchase price for a home can Duane afford:-

Since, Duane pays off his auto loan thereby eliminating the $675 monthly payments and therafter he has only housing debt payment and its related expenses to pay, thus he will be covered in 28% rule.

Maximum debt service amount = Annual Gross income*28%

=$45,000*28%

= $12,600

Debt payment available for housing loan = $12600 - $3000

= $9600

Monthly home loan payment = $9600/12

= $800

Using, the monthly payment to calculate the Home loan amount:-

where, P = loan amount

r = Periodic Interest rate =7.5%/12 = 0.625%

n= no of periods =30yrs*12 = 360

EMI = monthly payment = $800

P = $ 114414.10

Loan amount = $ 114414.10

Down-payment = 20%

Maximum purchase price of home = Loan amount/(1-Down-payment)

= $114414.10/(1-0.20)

= $ 143,017.62

So, maximum purchase price for a home can Duane afford is $ 143,017.62

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