Question

the guenthers gross monthly income is $6700. they have 18 remaining payments of $220 on a new car. they are applying for a 20-year, $174,000 mortgage at 7.0%. the taxes and insurance on the house are $390 per month. the bank will only approve a loan that has a total monthly mortgage payment of principal, interest, property taxes, and homeowners insurance that is less than or equal to 28% of their adjusted monthly income. complete parts (a) through (c) below.
click the icon to view the table of monthly payments.

a) determine 28% of the guenthers adjusted monthly income.
$ (round to the nearest cent.)

b) determine the guenthers total monthly mortgage payment, including principal, interest, taxes, and homeowners insurance.
$ (round to the nearest cent.)

c) do they qualify for this mortgage?
no
yes

Explanation:

Calculate adjusted monthly income

To find the adjusted monthly income, we subtract any long-term monthly debt payments (such as car payments) from the gross monthly income.

• Gross monthly income: \(I_{\text{gross}} = \$6700\)
• Car payment: \(P_{\text{car}} = \$220\)
• Adjusted monthly income:

$$ I_{\text{adjusted}} = \$6700 - \$220 = \$6480 $$

Determine 28% of adjusted monthly income

We calculate 28% of the adjusted monthly income to find the maximum allowable monthly housing payment under this guideline.

$$ \text{Limit}_{28\%} = 0.28 \times \$6480 = \$1814.40 $$

Calculate monthly mortgage payment

The total monthly mortgage payment consists of the principal and interest (P&I) payment plus monthly taxes and insurance.

1. Find the P&I payment for a 20-year, \$174,000 mortgage at 7.0%. Using the standard amortization formula:

$$ M = P \frac{r(1+r)^n}{(1+r)^n - 1} $$

where \(P = 174000\), \(r = \frac{0.07}{12} \approx 0.00583333\), and \(n = 20 \times 12 = 240\).

$$ M = 174000 \times \frac{0.00583333(1.00583333)^{240}}{(1.00583333)^{240} - 1} \approx \$1349.02 $$

1. Add the monthly taxes and insurance of \$390:

$$ \text{Total Payment} = \$1349.02 + \$390.00 = \$1739.02 $$

Determine mortgage qualification

Compare the total monthly mortgage payment to the 28% limit of the adjusted monthly income.

• Total monthly mortgage payment: \$1739.02
• 28% limit: \$1814.40

Since \(\$1739.02 \le \$1814.40\), the payment is less than or equal to 28% of their adjusted monthly income. Therefore, they qualify.

Answer:

Question a

Determine 28% of the Guenthers' adjusted monthly income.
<blank>\$1814.40</blank>

Question b

Determine the Guenthers' total monthly mortgage payment, including principal, interest, taxes, and homeowners' insurance.
<blank>\$1739.02</blank>

Question c

Do they qualify for this mortgage?

• Yes (Correct answer)
• No