It is January 2024. You are married with two small children (6 and 2). You want to save enough money to send your two children to university. Since they are four years apart in age, you need to have a sum of money that will provide $4 000 semiannually for eight years. Your household’s annual net income is $67 500. The two of you accumulated $67 000 in student loans to be paid back in maximum 15 years at 6.5% interest rate. You have the following fixed monthly expenses (at least): 1. Rent (includes utilities): 1200+ 2. Daycare: 650+ 3. 

Two cars (3y & 7y) insurance and maintenance: 450+ 4. Phone, TV, internet, etc.: 200+ 5. Food, clothing, etc.: 950+ 6. Entertainment, holiday, unforeseen expenses etc.: 500+ At the moment you have $10 000 in savings. You are thinking of purchasing a home worth between $350 000 and $400 000 by paying x% down and then taking out a mortgage at j2 = 3.5%. (Typically lenders will require mortgage loan insurance if a borrower has a down payment of less than 20% of the purchase price of the home.) Your (initial) plan is to amortize the mortgage over 25 years with equal monthly payments. (Think about all the additional monthly expenses of owning a house: for example 

* Utilities: $350+; 

* Maintenance: $200+; 

* Property tax: $350+; 

*Home Insurance: $150+; 

*$$$ Mortgage loan insurance: depending on down payment) Your overall goal should be to reduce total interest payment by as much as possible. (at its core this is the basis of the marking scheme) PART A 

a. Determine the ideal/optimal year of buying a house, the total amount you can afford under the above circumstances and the down payment (this might require more than one scenario). 

b. Determine the monthly payment and create amortization schedules showing the distribution of the payments as to interest and principal. PART B For the above problem answer the following questions using your initial data set. For full marks show your calculations (i.e. solve it manually on paper). 

A) Determine the monthly rate i12 = ? 

B) Determine the monthly payment R = ? 

C) How much interest is repaid in the 36th payment? I36 = ? 

D) How much principal is repaid in the 142nd payment? Pr142 = ? 

E) What is the outstanding balance of the loan after the 187th payment? OB187 = ? 

F) Determine your (buyer’s) equity at the end of 8 years. BEQ = ? 

G) Determine the seller’s equity at the end of 22 years. SEQ = ? 

H) Find the Total Amount Repaid during the lifetime of the loan. 

I) Find the Total Amount of Interest during the lifetime of the loan.