There are two more topics to examine to conclude our section on Mortgages. The first is the 32% rule, which states that no more than 32% of your gross monthly can go towards housing costs. The second (and final topic) will be how to calculate accelerated bi-weekly payments and savings when choosing to make accelerated bi-weekly payments.

The 32% Rule

Your housing costs shouldn’t be more than 32% of your gross monthly income.^[1] Housing costs include your mortgage payment, property taxes, heating costs and half of your strata (condo) fees.^[2]

PMT + Prop Taxes + Heat Costs + 0.5 × Strata Fees ≤ 0.32(Gross Monthly Income)

We can rework this formula to determine the maximum allowable monthly mortgage payment:

[latex]\begin{align*} \textrm{PMT} & ≤ 0.32 (\textrm{Gross Monthly Income}) - (\textrm{Prop Taxes + Heat Costs + 0.5 × Strata Fees})\\ & ≤ 0.32 \textrm{(Gross Monthly Income) - Prop Taxes - Heat Costs} - 0.5 × \textrm{Strata Fees}\\ \end{align*}[/latex]

Let us now use this rule to determine how much Brenda and Huong will be allowed to borrow when they go to purchase an apartment in Central Surrey.

Example 5.11.1

Huong and Brenda are looking to purchase a 2-bedroom apartment in Central Surrey.  The sisters’ combined gross income is $150,000.  The property taxes on the 2 bedroom apartment are $3,600/year.  The average heating cost is $43/month.  The strata fee for the apartment is $500/month.  What is the largest mortgage payment Brenda and Huong would be allowed to make per month?

Let us use the 32% rule to determine Huong and Brenda’s maximum allowable mortgage payment. To use the rule, we need all housing expenses monthly. Let us calculate the equivalent monthly amounts for Huong and Brenda’s income and their potential property taxes:

[latex]\textrm{Gross Monthly Income} = \frac{\$150,000}{12} = \$12,500[/latex]

[latex]\textrm{Monthly Property Taxes} = \frac{\$3,600}{12} = \$300[/latex]

This gives the following for the maximum allowable mortgage payment:

[latex]\begin{align*} PMT & ≤ 0.32 \textrm{(Gross Monthly Income)} -\textrm{Prop Taxes – Heat Costs}- 0.5(\textrm{Strata Fees})\\ & ≤ 0.32($12,500) - $300 - $43 - 0.5($500)\\ & ≤ $3407 \end{align*}[/latex]

Conclusion: Huong and Brenda can pay no more than $3,407 per month on their mortgage payment.

Example 5.11.2

Huong and Brenda have $100,000 saved up for a down payment on an apartment. The current interest rate is 2.4% compounded semi-annually for a fixed rate 25 year mortgage with a 5-year term. What is the most expensive apartment Brenda and Huong would be allowed to purchase?

Let us use the maximum allowable monthly mortgage payment (PMT) from Example 1 to calculate the maximum Huong and Brenda are allowed to borrow (PV):

Huong and Brenda can borrow $769,071.85. To determine price of the most expensive apartment, include the down payment:

[latex]\begin{align*} \textrm{Max Allowable Price} &= \textrm{Max Amount Borrowed} + \textrm{Down Payment} \\&= \$769,071.85+\$100,000 \\&= \$869,071.85 \end{align*}[/latex]

Conclusion: Huong and Brenda can buy an apartment costing up to $869,071.85.

Bi-weekly & Accelerated Bi-Weekly Payments

A bi-weekly payment is a payment that occurs once every 2 weeks.  Bi-weekly payments are popular because people are commonly paid bi-weekly.  There are 26 bi-weekly payment periods in a year.

When paying bi-weekly, people can choose the accelerated bi-weekly option. When they choose an accelerated bi-weekly mortgage, they pay half of the normal monthly payment every two weeks. When making this choice, they end up making 2 extra bi-weekly payments per year. This happens because for two of the twelve months in the year, the borrower will receive three paychecks during that month. This happens in months where their payday lands on the following days^[3]:

• The 1^st, 15^th and 29^th of the month
• The 2^nd, 16^th and 30^th of the month

Those two extra bi-weekly payments equal to one extra full-sized monthly mortgage payment. This overpayment by one full-sized mortgage payment per year will lead to savings in interest paid on the mortgage and the time required to pay off the mortgage.

Let us look again to Huong and Brenda and their mortgage options when they purchase an apartment in Central Surrey.

Example 5.11.3

Huong and Brenda have found the perfect apartment! It costs $850,000 and they will make a $100,000 down payment. Now they just need to decide whether to make monthly mortgage payments or accelerated bi-weekly mortgage payments.

Help them decide by determining the size of the mortgage payments for both options as well as the potential time and money saved if Huong and Brenda make accelerated bi-weekly payments (if they can afford it)!

Let us start by calculating the size of Huong and Brenda’s monthly mortgage payments.

Example 5.11.3a – The Size of Huong and Brenda’s Monthly Payments

Step 0: Determine the amount Huong and Brenda will borrow:

[latex]\begin{align*} \textrm{Amount Borrowed} &= \textrm{Selling Price} - \textrm{Down Payment} \\&= \$850,000-\$100,000 \\&= \$750,000 \end{align*}[/latex]

Step 1: Determine the size of the regular monthly mortgage payments (assume Huong and Brenda will still have a 25-year mortgage and be charged 2.4%, compounded semi-annually):

Conclusion: If Huong and Brenda make monthly payments, they will pay $3,323 per month.

Example 5.11.3b – Total payments Per Year (Monthly)

Let us now calculate how much Huong and Brenda will make in mortgage payments per year:

[latex]\textrm{Total Payments per Year} = \$3323 \times 12 = \$39,876[/latex]

Conclusion: Huong and Brenda will make $39,876 in mortgage payments each year if they pay monthly.^[4].

Example 5.11.3c – Total Interest Paid with Monthly Payments

Now that we have the size of Huong and Brenda’s monthly payments, we can calculate the interest they will pay over the 25 years. We will assume, to avoid making this example too long, that the interest rate will remain fixed at 2.4% for the entire 25 years.

Step 1: Make sure all values from example 3a are still in your BAII Plus (TVM keys).

Step 2: Round up the payment and re-enter as a negative value: 3323 + | − PMT

Step 3: Access the AMRT menu: 2ND PMT

Step 4: Input P₁: 1 ENTER   ↓  

Step 5: Input P₂: 300 ENTER   ↓  

Step 6: Scroll down   ↓     ↓     ↓   to INT: −246,699.76

Conclusion: Huong and Brenda will pay $246,699.76 in interest if they choose to make monthly payments.

Example 5.11.3d – Time-Savings with Accelerated Bi-Weekly

When making accelerated bi-weekly payments, we divide the regular monthly payments in half:

[latex]\textrm{Accelerate Bi-Weekly Payment} = \frac{\$3,323}{2}=\$1,661.50[/latex]

We then enter this payment amount into the BAII Plus:

It will take them 583 full-sized and one smaller payment to pay off the mortgage with accelerated bi-weekly payments. This will still be 584 payments (even though the last one is smaller, it still counts as a payment). Let us calculate how many years that is:

[latex]\textrm{Number of Years} = \frac{584}{26}=22.46 \textrm{ years}[/latex]

It will take them 22.46 years to pay of their mortgage with accelerated bi-weekly payments. Let’s compare that to the time required to pay off the mortgage with monthly payments:

[latex]\textrm{Time Saved} = 25 - 22.46 = 2.54 \textrm{ years}[/latex]

Conclusion: Huong and Brenda will save 2.54 years if they choose to make bi-weekly payments.

Example 5.11.3e – Additional Amount Paid per Year with Accelerated Bi-Weekly

Let us now calculate how much Huong and Brenda will make in bi-weekly payments per year:

[latex]\textrm{Total Payments per Year} = \$1661.50 \times 26 = \$43,199[/latex]

Compare this amount to the total paid with monthly payments to determine how much more they will pay per year if they make accelerated bi-weekly payments:

[latex]\textrm{Extra Amount Paid} = \$43,199 - \$39,876 = \$3,233[/latex]

Conclusion: Huong and Brenda pay an extra $3,233 in mortgage payments if they make accelerated bi-weekly payments. Notice that this is exactly equal to one monthly payment.

Example 5.11.3f — Savings in Interest with Accelerated Bi-Weekly

Steps 0-2: Check that all values for Example 3d are still in your BAII Plus.

Step 3: Access the AMRT menu: 2ND PMT

Step 4: Input P₁: 1 ENTER   ↓  

Step 5: Input P₂: 584 ENTER   ↓   (There are 584 bi-weekly payments in total).

Step 6: Scroll down   ↓     ↓     ↓     INT: −218,915.65

Huong and Brenda will pay $218,915.65 in interest if they make accelerated bi-weekly payments. We can use this amount to figure out their savings in interest with this payment plan:

[latex]\textrm{Money Saved} = \$246,699.76 - \$218,915.65 = \$27,784.11[/latex]

Conclusion: Huong and Brenda will save $27,784.11 in interest if they pay with accelerated bi-weekly payments instead of monthly payments.

Example 5.11.3g — What Should Huong and Brenda Decide?

If Huong and Brenda can afford to pay the extra $3,233 per year, then they should choose the accelerated bi-weekly payment option and save 2.54 years and $27,784.11 in interest when repaying their mortgage!

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