Question

A man is looking to purchase a home in the Cleveland Suburbs. He has enough for a 20% down payment and an income of $70,000 per year. His FICO Score is 660. The prime Interest Rate for 30-year Mortgages is 5%. He has a car payment of $400 per month and a Student Loan Payment of $200 per month. The home he 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 man pay for the home? How large of a mortgage will the bank allow him take out?

Answer 1

Solution:

Monthly Car Payment = $400
Interest rate = 5% per annum or monthly 0.4167% or 0.0042
Period = 30 years or 360 months (i.e 12 x 30)
Total payment of loan can be found by applying the future value of an annuity
Total Payment = A x (1+R)ⁿ​ -1/R where A = annuity i.e 400; R = monthly rate of interest i.e 0.0042;
period (n) = 360
    = 400 x (1+0.0042)³⁶⁰​-1/0.0042
                        = (400 x 4.52145418 -1)0.0042
                        = 400 x 3.5214518/0.0042
                        = 1408.58/0.0042
                        = $335,376
Hence, total payment on car is $335,376
Now we have to calculate Principal amount in the total payment of $335,376, that can be calculated by applying the following formula

Principal = A x 1-(1+R)^-n​/R
Principal = 400 x (1 - (1+0.0042)^-360​/0.0042)
Principal = 400 x (1- 0.221167784/0.0042) = 400 x (.778832216/0.0042)
Principal = 400 x (0.7788/0.0042) = 400 x 185.42857 = $$74.171.43
Hence, the principal amount in the loan is $74,171 whcih is after payment of 20% down payment. The principal amount is equal to 80% of the loan.
So the total loan will be $74171/80% = $92,713.75