Let's break down this problem into two parts.

Part (i): Determine how much of a monthly mortgage Tobin and Joanne can afford.

To determine how much Tobin and Joanne can afford for their monthly mortgage, we will use the Total Expense Ratio (TER), which is typically about 36% of their gross monthly income for housing and other debts.

Step 1: Calculate their total gross monthly income.

$\text{Monthly Gross Income} = \frac{\text{Annual Gross Income}}{12} = \frac{120,000}{12} = 10,000$

Step 2: Apply the Total Expense Ratio (TER).

We assume the maximum total expenses should not exceed 36% of their gross monthly income. $\text{Max Expenses} = 36\% \times 10,000 = 0.36 \times 10,000 = 3,600$

Step 3: Subtract other monthly expenses to find the maximum mortgage payment.

Their monthly expenses include:

• Property taxes: $\frac{1350}{12} = 112.50$ per month
• Insurance: $\frac{1820}{12} = 151.67$ per month
• Car payment: $250$ per month
• Student loan payments: $285$ per month

Now, let's calculate the total of these monthly expenses: $\text{Total Monthly Non-Mortgage Expenses} = 112.50 + 151.67 + 250 + 285 = 799.17$

Subtracting this from the maximum allowable expenses: $\text{Maximum Monthly Mortgage Payment} = 3,600 - 799.17 = 2,800.83$

Thus, Tobin and Joanne can afford a monthly mortgage payment of $2,800.83.

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Part (ii): Determine how much house they could afford using Excel's PV function.

The mortgage formula (PV) calculates the present value (amount of house) that can be financed with a given monthly payment, interest rate, and loan term.

The Excel function to calculate the present value is: $\text{PV}(\text{rate}, \text{nper}, \text{pmt})$ Where:

• rate is the monthly interest rate (annual interest rate divided by 12).
• nper is the total number of payments (loan term in years times 12).
• pmt is the monthly mortgage payment (which we've calculated as $2,800.83).

Step 1: Identify the known values.

• Annual Interest Rate (APR): 4.65% or 0.0465
• Monthly Interest Rate: $\frac{0.0465}{12} = 0.003875$
• Number of Payments (nper): $10 \times 12 = 120$ (since it's a 10-year mortgage)
• Monthly Payment (pmt): $-2,800.83$ (note: this value is negative in the formula since it's an outflow)

Step 2: Apply the formula.

We can plug these into Excel's PV function: $\text{PV}(0.003875, 120, -2800.83)$

This gives us the total value of the house that Tobin and Joanne can afford.

Let me calculate that for you.Tobin and Joanne can afford a house priced at approximately $268,373.86 based on their monthly mortgage payment of $2,800.83 and a 10-year mortgage at a fixed rate of 4.65%.

Would you like further clarification on any part of the process or more details? Here are some related questions to expand your understanding:

1. How would the affordable house price change if the interest rate increased to 5%?
2. What happens to the affordability if Tobin and Joanne extend the mortgage to 15 years instead of 10?
3. How would a higher total expense ratio (e.g., 40%) affect their maximum affordable monthly payment?
4. What is the impact of additional monthly expenses on their mortgage affordability?
5. How does the mortgage rate affect the overall interest paid over the loan's duration?

Tip: Always check different mortgage options (fixed vs. variable rates) to see which one aligns best with your long-term financial goals!