Question

Two years ago, after you graduated from college and landed a job where you are earning $76,500 a year, you purchased a car from your uncle and have been paying $300.00 a month. You have another year to go. You are now ready to participate in the American Dream and contemplate buying a house. Current 30-year mortgage rates are at a low annual rate of 3.25%. Your monthly mortgage payment cannot be more than 34% of your gross monthly income. Furthermore, a 10% down payment and 7% closing costs are required on any house that you buy. You want to buy the house on the corner of Elm Street. The mortgage company has approved your loan. When you tell the mortgage officer about your $300 car payment, he says “If it doesn't show up on your credit report, we don't have to consider it. And it will be gone in a year anyway". You know that the required mortgage payment will be almost impossible to pay until you finish paying car payments, but you don't want to wait another year because you fear that interest rates and house prices might go up.

       Answer the following questions:         

1. What would be the required Mortgage Payments for the House? (2) ___________________

2. What is the amount of the Mortgage Loan? (2) _________________________

3. What is the maximum amount that you can offer for the House? (3)

_______________________

4. How much do you need for the Down Payment? (1)        ______________________

5. How much do you need for the Closing Costs if the Closing Costs are based upon the cost of the house?   (1)       

                                                      __________________           

6. What is the total amount of Interest that you will have paid at the end of the Mortgage Loan if you make all of the required payments as agreed for the full 30 years? (1)

               _________________________________

Answer 1

a) The following facts needs to be considered:

- One year car payments are still remaining

- Mortgage payment cannot be made is car EMI is paid

- Your mortgage cannot exceed 34% of gross Income. Hence:

a) Gross Income	76,500
b) Car EMI	3,600
c) Income available for other expenses / savings	72,900
d) Max Mortgage (34% of a)	26,010
e) Hence, other non avoidable exp / savings (a-d+b)	54,090
f) Hence, Mortgage Amount (d-b) / month	22,410

b) Assuming that the monthly mortgage payment for house includes interest portion (Similar to EMI). The mathematical formula for EMI is

EMI = [P*R*(1+r)^n]/[(1+r)^n-1], where P stands for loan, R for monthly rate and n for months

Hence, P = [EMI* (1+r)^n-1]/R*(1+r)^n

= {22410*(1+(3.25/1200))^359}/(3.25/1200)*((1+(3.25/1200)^360)

= $82,52,112

c)

Loan Amount	82,52,112
Down Payment (8252112/90*10)	9,16,901.33
Maximum Amount that you can offer for house now	91,69,013

d) Down payment = 10% of House Value = $9,16,901

e) Closing cost = 7% of the House Cost = 91,69,013*7% = $6,41,831