MAT133Y5 Assignment 01

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1 Staple Here Score: / MAT133Y Assignment 01 Family Name: Given Name: Indicate the tutorial in which you are enrolled: TUT01 TUT02 TUT03 TUT04 TUT0 TUT08 T T1600 T00 W0900 W00 W10 TUT09 TUT0111 TUT0112 TUT0114 TUT0116 TUT0117 W1600 W1700 R10 R1300 R1400 R00 TUT0118 TUT0119 TUT01 TUT0121 TUT0122 TUT0123 R1800 R1600 R1700 R1900 F00 F Answer the questions in the space provided. If you run out of room for an answer, continue on the back side of the sheet or attach a sheet of paper detailing your work, clearly indicating when you ve done so. You are expected to show all work unless otherwise indicated. Due at the beginning of tutorial in which you are enrolled in the week of October 2.

2 The average price of a Mississauga home is $70, 000. In this assignment, we ll take an idealized look at the return on investment for purchasing a home versus renting. We will ignore things like variability in interest rates, the housing market, and capital gains, but will still arrive at a reasonable estimate. Round your final answers to the nearest cent (two decimal places). 1. [2 marks] Determine the monthly payment required to amortize a $70, 000 mortgage over a 2 year period if you put a % down payment on your home, at an annual interest rate of 4.7% (the Canadian year fixed-rate average) compounded monthly. 2. [3 marks] Determine the principal remaining in the loan after,,,, 2 years. Show the calculation for years below, then fill in the provided table with the other values. Outstanding Principal 2 1

3 3. [3 marks] The 30 year annualized increase in housing prices in the GTA is 3.7% per annum. Determine the market value of your home after,,,, 2 years. Show your computation for the year market value, then fill in the table. Market Value 2 4. [1 mark] If you sell your house at market value after k-years, your return on investment is the sale price of your home, less the outstanding principal on the mortgage. Fill in the table below with your return on investment if you sell after,,,, 2 years. This is just subtraction, so there s no need to show your work. Return 2 2

4 . [1 mark] Let s now assume you rent instead of buy. You will invest all money that you would have spent on mortgage payments, property taxes, and maintenance. Mississauga property taxes amount to 0.92% of the value of your home per year. The table below gives the effective average property tax you pay over the span of n years. For example, in the first years, you pay on average $8170/year in property taxes. 2 Average Property Tax (T ) $7430 $8170 $9008 $9960 $140 For simplicity, we ll assume that annualized property maintenance amounts to $700 per year scaled to inflation (2%), giving the following table: 2 Average Maintenance Costs (C) $7806 $8212 $8646 $9111 $9609 Let s assume you rent a 2 bedroom apartment in 17 for the Mississauga average $1600/month and never move. Rent increases for Ontario have averaged 2% over the last years. We ll use the following chart for your average yearly rent: 2 Average Yearly Rent (R) $19, 983 $21, 024 $22, 13 $23, 326 $24, 600 Combined with your yearly mortgage payment of 12M (where M is your solution to Question 1), the average amount of money you can invest yearly is Fill in the table below: 2 Average Yearly Investment (I) I = 12M + T + C R 3

5 6. [ marks] Your solutions for Question () should average about $36, 400, so to make our lives easier we ll assume you invest your down payment of $0, 000, plus $3000/month. Over the last 0 years, the equities market has grown at an annualized rate of 8.0%, compounded monthly. Assume you invest in a fund which matches the growth of the market (say an index fund tracking the S&P00). Compute your investment earnings at the,,,, 2 year mark, compounded monthly. Show the explicit computation for years, then fill in the table below. 2 Investment Earnings Note: An important point we ve ignored is taxes. For example, you do not pay a capital gains tax when selling your principal residence. Therefore, the numbers shown in Question 4 are tax exempt. On the other hand, the solutions to Question 6 are not tax free in general. Assuming an income of $170, 000 to qualify for the given loan, about % of your investments are non-registered (that is, not tax-deferred or tax-sheltered). Additionally, some of that income will be dividend payments. Dividends from qualified Canadian companies are privileged in taxes, and only half of your capital gains are taxed when you sell the underlying asset, while all other dividends are taxed at your marginal rate. It s difficult to say what the effective tax rate would be on your earnings from Question 6, but it s fair to say it makes a significant impact on the actual earnings. 4