Question

Advice from most financial advisers states to spend no more than​ 28% of​ one's gross monthly income for​ one's mortgage​ payment, and to spend no more than​ 36% of​ one's gross monthly income for​ one's total monthly debt. If a​ family's gross annual income is ​$33,600​, use appropriate computations to determine whether the family can afford a ​$240,000 40​-year ​fixed-rate mortgage at 4​%.
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Part 1
Choose the correct answer below.
A.
The family can afford the mortgage because the monthly payment is greater than what they should pay each month.
B.
The family cannot afford the mortgage because the monthly payment is greater than what they should pay each month.
C.
The family cannot afford the mortgage because the monthly payment is less than what they should pay each month.
D.
The family can afford the mortgage because the monthly payment is less than what they should pay each month.

Answer 1

Monthly gross income = 33,600/12 = $2,800.

Maximum mortgage payment (28%) = 0.28(2,800) = $784.
Maximum total debt (36%) = 0.36(2,800) = $1,008.

Monthly mortgage payment for a $240,000 loan, 40 years (480 months), 4% APR:
i = 0.04/12 = 0.0033333; n = 480.
Payment = L * [i / (1 - (1+i)^(-n))] ≈ 240,000 * 0.004183 ≈ $1,004.

Since $1,004 > $784 (the 28% mortgage limit), the family cannot afford the mortgage under the usual guideline (even though $1,004 is just under the 36% total-debt limit).

Correct answer: B.