{"id":926,"date":"2020-08-10T13:31:16","date_gmt":"2020-08-10T17:31:16","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&p=926"},"modified":"2021-07-15T12:00:14","modified_gmt":"2021-07-15T16:00:14","slug":"debt-service-ratio","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/debt-service-ratio\/","title":{"raw":"5.11 The 32% Rule and Bi-Weekly Payments","rendered":"5.11 The 32% Rule and Bi-Weekly Payments"},"content":{"raw":"
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Learning Outcomes<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nUse the 32% rule to determine the maximum mortgage amount. Also, calculate the size of accelerated biweekly mortgage payments or the savings in interest.\r\n\r\n<\/div>\r\n<\/div>\r\nThere 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.\r\n

The 32% Rule<\/h1>\r\nYour housing costs shouldn't be more than 32% of your gross monthly income.[footnote]This rule is also called the GDS - Gross Debt Service Ratio.[\/footnote] Housing costs include your mortgage payment, property taxes, heating costs and half of your strata (condo) fees.[footnote]There is also the Total Debt Service Ratio (TDS) that lenders use when borrowers have other loans. No more than 40% of a borrower's income can go towards their mortgage payment, property taxes, heating costs, half of their strata fees and other debt payments. They will take the minimum payment generated by the GDS (32%) and TDS rules.[\/footnote]\r\n

PMT + Prop Taxes + Heat Costs + 0.5 \u00d7 Strata Fees \u2264 0.32(Gross Monthly Income)<\/p>\r\nWe can rework this formula to determine the maximum allowable monthly mortgage payment:\r\n

[latex]\\begin{align*}\r\n\\textrm{PMT} & \u2264 0.32 (\\textrm{Gross Monthly Income}) - (\\textrm{Prop Taxes + Heat Costs + 0.5 \u00d7 Strata Fees})\\\\\r\n& \u2264 0.32 \\textrm{(Gross Monthly Income) - Prop Taxes - Heat Costs} - 0.5 \u00d7 \\textrm{Strata Fees}\\\\\r\n\\end{align*}[\/latex]<\/p>\r\nLet 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.\r\n

Example 5.11.1<\/h2>\r\n

Huong and Brenda are looking to purchase a 2-bedroom apartment in Central Surrey.\u00a0 The sisters\u2019 combined gross income is $150,000.\u00a0 The property taxes on the 2 bedroom apartment are $3,600\/year.\u00a0 The average heating cost is $43\/month.\u00a0 The strata fee for the apartment is $500\/month.\u00a0 What is the largest mortgage payment Brenda and Huong would be allowed to make per month?<\/p>\r\nLet us use the 32% rule<\/span>\u00a0to 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:\r\n

[latex] \\textrm{Gross Monthly Income} = \\frac{\\$150,000}{12} = \\$12,500 [\/latex]<\/p>\r\n

[latex] \\textrm{Monthly Property Taxes} = \\frac{\\$3,600}{12} = \\$300 [\/latex]<\/p>\r\nThis gives the following for the maximum allowable mortgage payment:\r\n

[latex]\\begin{align*}\r\nPMT & \u2264 0.32 \\textrm{(Gross Monthly Income)} -\\textrm{Prop Taxes \u2013 Heat Costs}- 0.5(\\textrm{Strata Fees})\\\\\r\n& \u2264 0.32($12,500) - $300 - $43 - 0.5($500)\\\\\r\n& \u2264 $3407\r\n\\end{align*}[\/latex]<\/p>\r\n\r\nConclusion<\/span>: Huong and Brenda can pay no more than $3,407<\/span> per month on their mortgage payment.\r\n\r\n \r\n

Example 5.11.2<\/h2>\r\nHuong 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?\r\n\r\nLet us use the maximum allowable monthly mortgage payment (PMT) from Example 1 to calculate the maximum Huong and Brenda are allowed to borrow (PV):\r\n\r\n\r\n\r\n\r\n\r\n
B\/E<\/th>\r\nP\/Y<\/th>\r\nC\/Y<\/th>\r\nN<\/th>\r\nI\/Y<\/th>\r\nPV<\/th>\r\nPMT<\/th>\r\nFV<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
END<\/td>\r\n12<\/td>\r\n2<\/td>\r\n25\u00d712=300<\/td>\r\n2.4<\/td>\r\nCPT<\/strong> +769,071.85<\/td>\r\n\u22123,407<\/span><\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nHuong and Brenda can borrow $769,071.85<\/span>. To determine price of the most expensive apartment, include the down payment:\r\n

[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]<\/p>\r\nConclusion: <\/span>Huong and Brenda can buy an apartment costing up to $869,071.85<\/span>.\r\n\r\n \r\n

Bi-weekly & Accelerated Bi-Weekly Payments<\/h1>\r\nA bi-weekly payment is a payment that occurs once every 2 weeks.\u00a0 Bi-weekly payments are popular because people are commonly paid bi-weekly.\u00a0 There are 26 bi-weekly payment periods in a year.\r\n\r\nWhen paying bi-weekly, people can choose the [pb_glossary id=\"936\"]accelerated bi-weekly[\/pb_glossary] 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[footnote]Their payday could also land on the 3rd<\/sup>, 17th<\/sup> and 31st<\/sup> of the month. This is more rare because only 7 months in the year have 31 days and February only has 28 days, normally. In general, there will be two months in the year where they have three paychecks.[\/footnote]:\r\n