Question

Sarah’s gross salary is $200,000 per year. She is interested in purchasing a $600,000 house. She will make a down payment of 20% and take out a 15 year, 4.5% fixed rate mortgage. The taxes plus insurance is $8000. In addition, she has student debt and makes annual payments of $6000 per year. What is the Gross Debt Service and Total Debt Service ratio? If the bank requires that these ratios must be less than 30 and 35% respectively, can she obtain her mortgage?

Answer 1

Sarah's Gross debt service ratio = (Annual mortgage payment + Annual taxes plus insurance on the property)/ annual gross income

We know that the cost of house is $600,000 and down payment is 20%

Therefore Amount of mortgage after 20% of down payment

= $ 600,000 * (1-20%)

= $ 600,000 * 0.8 = $480,000

A 15-year mortgage at fixed-rate of 4.5%

The formula for monthly payment

M = P * (1+r) ^n * r / [(1+r) ^n - 1]

Where M = monthly payment

P = mortgage amount or principal = $480,000

And r = monthly interest rate = annual interest rate/12 = 4.5%/12 = 0.375%

And n = number of months = 15 years *12 = 180 month

Therefore

M = $480,000 * (1+0.375%) ^180 *0.375 / [(1+0.375) ^180 – 1] = $3,671.97

Annual mortgage payment = monthly payments *12

=$3,671.97 *12

= $44,063.61

Annual taxes on the property = $8000

Annual gross income = $200,000

Therefore

The Sarah's Gross debt service ratio = ($44,063.61 + $8000) /$200,000

= 0.2603 or 26.03%

Sarah's Total debt service ratio = (Annual mortgage payment + Annual taxes plus insurance on the property + other loan payments)/ annual gross income

As she has student debt and makes annual payments of $6000 per year therefore other loan payments are $6000 per year

Therefore,

Sarah's Total debt service ratio = ($44,063.61 + $8000 + $6000) /$200,000

=$58,063.61/$200,000

= 0.2903 or 29.03%

If the bank requires that these ratios must be less than 30 and 35% respectively, then also she can obtain her mortgage as her gross debt service ratio is 26.03% (less than 30%) and Total debt service ratio is 29.03% (less than 35%)