Suppose you take out a 20-year mortgage for a house that costs $317760. Assume t
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Question
Suppose you take out a 20-year mortgage for a house that costs $317760. Assume the following:
The annual interest rate on the mortgage is 4%.
The bank requires a minimum down payment of 18% at the time of the loan.
The annual property tax is 2.4% of the cost of the house.
The annual homeowner's insurance is 1.2% of the cost of the house.
The monthly PMI is $74
Your other long-term debts require payments of $775 per month.
If you make the minimum down payment, what is the minimum gross monthly salary you must earn in order to satisfy the 28% rule and the 36% rule simultaneously?
Explanation / Answer
Cost of the House = $317760
Minimum down payment @ 18% = $57196.80
Annual Interest Rate (APR) = 4%
Number of years (n) = 20
= 240 months
Principal (P) = Cost of the house - Down payment paid
= $317760 - $57196.80
= $260563.20
Monthly Installment = [(APR/12)*P*(1 + (APR/12)n )]/[(1+(APR/12)n)-1]
After inserting all the values mentioned above, we get
= [(4/12)*260563.20*(1+(4/12)240)]/[(1+(4/12)240)-1]
=[(1/3)*(26056320/100)*(1 + (1/3)240)]/[(1+(1/3)240)-1]
= 1578.96
Monthly installment comes out to be $ 1578.96
Now to calculate monthly taxes
Annual Property tax = 2.4%
Monthly Property Tax = 2.4/12=0.20%
Annual House Insurance = 1.2%
Monthly House Insurance = 1.2/12 = 0.10%
PMI = $74
Monthly PMI = $ 6.17
Total montly taxes, Insurance and PMI = $ 6.47
Total monthly installment = $1578.96 + $6.47
= $ 1585.43
Other monthly long-term debt payment =$775
For Housing Debt, Debt to Income ratio should be 28%, so calculating gross monthly salary required to satisfy 28% rule.
28% = Sum of monthly housing obligations/Gross monthly household income
28/100= Sum of monthly housing obligation/Gross monthly household income
28/100 = 1585.43/ Gross monthly household income
Gross monthly household income = 1585.43*100/28
= 5662.25
For Total Debt, Debt to Income ratio should not exceed 36%, so calculating gross monthly salary required to satisfy 36% rule.
36% = Sum of all monthly obligations (including housing and all other loans)/Gross monthly household income
36/100 = Sum of all monthly obligations /Gross monthly household income
36/100 = (1585.43 + 775)/Gross monthly household income
Gross monthly household income = 2360.43*100/36
= 6556.75
Taking the higher of the above two Gross monthly household income, minimum gross salary (monthly) should be $6556.75
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