Question

Suppose you take a 10-year mortgage for a house that costs $234,834. Assume the following: The annual interest rate on the mortgage is 3.3%. The bank requires a minimum down payment of 12% of the cost of the house. The annual property tax is 2% of the cost of the house. The annual homeowner's insurance is $863. The monthly PMI is $91. Your other long-term debts require payments of $1,589 per month. If you make the minimum down payment, what is the minimum gross monthly salary you must earn in order to satisfy the 36% rule? Round your answer to the nearest dollar.

Answer 1

Cost of the house = $ 234,834

Down-payment 12% = $ 234834 * 12% = $28,180

Loan (balance) = $234,834 - $28,180 = $206,654

Loan term =10 years with monthly payments , So, 10 * 12 = 120 payment periods

Annual interest on loan = 3.3%, so, monthly interest = 0.033/12 = 0.00275

Monthly Payment amount = Loan Amount / Discount factor

Discount factor = (((1+i)^N)-1) / (i(1+i)^N) = (((1+0.00275)^120-1)) / (0.00275(1+0.00275)^120)

Alternatively, we can use PMT function in excel with loan amount, periodic interest rate, and no. of payment periods, which yields us $2,024 as monthly payment in this question.

This $2024 is basically sum principal and interest on loan every month, though the portion of interest and principal in this payment will keep varying through the amortization period.

So, monthly EMI (P+I) = $2024

Annual property tax = 2% * 234834 = $4697

Monthly property tax = $4697 / 12 = $391

Annual insurance = $863

Monthly insurance = $863/12 = $72

Monthly PMI = $91

Monthly EMI on other long-term debts = $1589

Total monthly debt-related expenses = $2024 +$391 +$72 +$91 +$1589 = $4168

The 36% rule measures borrowers ability to afford mortgage considering his monthly gross income, his debt-related and other expenses. As per the rule, these expenses should not be more than 36% of income to be able to afford mortgage.

So, here minimum monthly income should be $4168 / 0.36 = $11,576