Question

Suppose you take out a 20-year mortgage for a house that costs $264,857. Assume the following:

The annual interest rate on the mortgage is 3%.

The bank requires a minimum down payment of 11% at the time of the loan.

The annual property tax is 2.5% of the cost of the house.

The annual homeowner's insurance is 0.9% of the cost of the house.

The monthly PMI is $87

Your other long-term debts require payments of $624 per month.

If you make the minimum down payment, what is the minimum gross monthly salary you must earn in order to satisfy the 28% rule and the 36% rule simultaneously? Round your answer to the nearest dollar.

Answer is $7,691 but unsure how to complete it

Answer 1

Answer: $7,691

Calculation:

28% rule and 36% rule means a household should spend no more than 28% of monthly income on household income and spend no more than 36% of monthly income on all debt, including the household expenses.

In this case, the monthly total expense is contributed by Property tax, PMI, Insurance, Other debt, and repayment of housing loan.

Annual property tax and insurance cost 2.5% and 0.9% of house costs respectively.

So, combined both costs 2.5 + 0.9 = 3.4% of 264,857 annually.

Which is $9,005.138 Converting into monthly expense = 9005.138 /12 = $750.43

Monthly PMI costs $87 and other long term debts = $624 per month.

While Monthly payment for the loan is $1,307.31 (Please find the calculation in the image attached below)

So, Total monthly Expense = $750.43 + $87 + $624 + $1,307.31 = $2,768.741

According to 36% rule, this should not exceed 36% of your total income,

So, your total income must be greater than $2,768.74 / 0.36 = $7,690.95

Which means your monthly income must be $7,691 to satisfy 36% rule.

Here we don't have much information about other household expenses. Considering household expenses $750 + $87 = $837. Income is far higher than satisfying 28% of the rule for this.

Hope this helps. If you need further clarification in any of the steps let me know through comment.

All the best!