4 You want to buy a house worth 4500000 and the a down payme

4. You want to buy a house worth $4,500,000, and the a down payment of 30% of the value of the house. lenders require that you make (i). Work out the amount of the mortgage loan that you will have to raise in order to buy the house. (1 point) Suppose you decide to finance the purchase with a 30-year fixed rate mortgage loan at a quoted rate of 3.6% per year with monthly payments. The lenders require that the amount of monthly payment is no larger than 29.7% of your monthly gross income. What must you earn on a yearly basis to qualify for the loan? (ii). (6 points) (ii). Assuming that you qualified for the loan, bought the house, and made your first payment on June 1, 2018, work out the percentage of the house you will own at the end of the year 2034 assuming that the value of house increases every month bv 0.3%

Solution

(a) House Price = $ 4500000, Down Payment = 30 % or 30 % of $ 4500000.

Down Payment Value = 0.3 x 4500000 = $ 1350000

Loan Amount = 4500000 - 1350000 = $ 3150000

(b) Interest Rate = 3.6 % per annum or 0.3 % per month, Loan Tenure = 30 years or 360 months

Let the monthly repayments be $ K

Therefore, 3150000 = K x (1/0.003) x [1-{1/(1.003)^(360)}]

K = $ 14321.33

K = 29.7 % of Monthly Gross Income

Monthly Gross Income = 14321.33 / 0.297 = $ 48219.97

Annual Income = 48219.97 x 12 = $ 578639.64

(c) Value of the House at the end of Year 2034 = 4500000 x (1.003)^(192) = $ 7998188.839

Mortgage Paid = 14321.33 x 192 = $ 2749695.36

Down Payment = $ 1350000

Total Repayment = 1350000 + 2749695.36 = $ 4099695.36

% of House Owned = 4099695.36 / 7998188.839 = 0.5126 or 51.26 % approximately.