Questions: The Guenthers' gross monthly income is 3700. They have 18 remaining payments of 390 on a new car. They are applying for a 30-year, 108,000 mortgage at 7.5%. The taxes and insurance on the house are 290 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.)

The Guenthers' gross monthly income is 3700. They have 18 remaining payments of 390 on a new car. They are applying for a 30-year, 108,000 mortgage at 7.5%. The taxes and insurance on the house are 290 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.)
Transcript text: The Guenthers' gross monthly income is $\$ 3700$. They have 18 remaining payments of $\$ 390$ on a new car. They are applying for a 30 -year, $\$ 108,000$ mortgage at $7.5 \%$. The taxes and insurance on the house are $\$ 290$ 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. $\$$ $\square$ (Round to the nearest cent.)
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Solution

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Solution Steps

Step 1: Calculate the Adjusted Monthly Income

The adjusted monthly income is calculated by subtracting the total monthly car payments from the gross monthly income: $3700 - $390 = $3310.

Step 2: Determine 28% of the Adjusted Monthly Income

28% of the adjusted monthly income gives the maximum allowable total monthly mortgage payment: 0.28 * $3310 = $926.8.

Step 3: Calculate the Monthly Principal and Interest Payment

Using the formula for a fixed-rate mortgage, the monthly principal and interest payment is calculated as: ($108000 * 0.00625) / (1 - (1 + 0.00625) ^ (-360)) = $755.15.

Step 4: Calculate the Total Monthly Mortgage Payment

The total monthly mortgage payment includes the monthly principal and interest payment plus monthly taxes and insurance: $755.15 + $290 = $1045.15.

Step 5: Compare the Total Monthly Mortgage Payment to the Maximum Allowable Payment

Since the total monthly mortgage payment of $1045.15 is greater than the maximum allowable payment of $926.8, the Guenthers do not qualify for the mortgage.

Final Answer:

The Guenthers do not qualify for the mortgage.

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