Question

1. Estimate the maximum house value you can afford to buy. Assume the mortgage is fixed rate, 30-year maturity, 80% LTV, with no points. The interest rate is quoted is 3.5% with monthly payments. The property tax rate in the city is 0.7% per year based on property value; the hazard insurance premium is 0.5% per year based on property value, and that on average you should consider $50 per month for maintenance. Determine the required monthly payment for the mortgage and the maximum house value you can afford if you buy. The monthly housing budget is $1,800

Answer 1

LTV is Loan-to-Value ratio which is equal to MA / APV

where MA = Mortgage Amount

APV = Appraised Property Value

Now let the Property value be 'x' and mortgage amount be 'y'.

Hence, 80% = y/x

Hence we can say that y = x*.8

Also to calculate the property value we can equate the total monthly expenses to $1800.

Hence,

monthly mortgage interest + property taxes + insurance premium + maintenance = $1800

y*.035/12 + x*.007/12 + x*.005/12 + 50 = 1800

Substituting y as x*.8

x*.8*.035/12 + x*.007/12 + x*.005/12 + 50 = 1800

x*.028 + x*.007 + x*.005 = 21000

x*.04 = 21000

x = $525000

Hence the maximum house value that we can afford to buy is $525000.

The mortgage amount will be 525000*.8 = $420000

Hence, monthly mortgage payment = 420000*.035/12 = $1225