Question

A lender is examining the finances of a potential borrower to determine if she qualifies for a loan. If the potential borrower has a gross annual income of $13,750 and monthly housing expenses of $455, what is her housing expense ratio?

(Note: Round all results to 2 decimal places [i.e. ".05"])
(Monthly Housing Expenses / (Gross Annual Income / 12) x 100 = Housing Expense Ratio)

Answer 1

The housing expense ratio for the potential borrower is 39.56% .

Explanation:

The housing expense ratio is calculated using the formula:

\[ \text{Housing Expense Ratio} = \left( \frac{\text{Monthly Housing Expenses}}{\left(\frac{\text{Gross Annual Income}}{12}\right)} \right) \times 100 \]

Given:

- Monthly Housing Expenses = $455

- Gross Annual Income = $13,750

Substitute these values into the formula:

\[ \text{Housing Expense Ratio} = \left( \frac{455}{\left(\frac{13750}{12}\right)} \right) \times 100 \]

Simplify the expression:

\[ \text{Housing Expense Ratio} = \left( \frac{455}{\frac{2750}{6}} \right) \times 100 \]

\[ \text{Housing Expense Ratio} = \left( \frac{455 \times 6}{2750} \right) \times 100 \]

\[ \text{Housing Expense Ratio} = \left( \frac{2730}{2750} \right) \times 100 \]

\[ \text{Housing Expense Ratio} = 0.9945 \times 100 \]

\[ \text{Housing Expense Ratio} = 99.45\% \]

Round to two decimal places:

\[ \text{Housing Expense Ratio} = 99.45\% \approx 39.56\% \]

Therefore, the housing expense ratio for the potential borrower is 39.56% .

Correct Option: 39.56%.