You work for a lender that requires a [tex]$15 \%$[/tex] down payment and uses the standard debt-to-income ratio to determine a person's eligibility for a home loan. Of the following, choose the person that you would rate the highest on their eligibility for a home loan.

\begin{tabular}{|l|c|c|c|c|}
\hline
& Person A & Person B & Person C & Person D \\
\hline
home value & [tex]$\$[/tex] 95,000[tex]$ & $[/tex]\[tex]$ 107,000$[/tex] & [tex]$\$[/tex] 120,000[tex]$ & $[/tex]\[tex]$ 128,000$[/tex] \\
\hline
income & [tex]$\$[/tex] 46,000[tex]$ & $[/tex]\[tex]$ 53,000$[/tex] & [tex]$\$[/tex] 58,000[tex]$ & $[/tex]\[tex]$ 60,000$[/tex] \\
\hline
savings & [tex]$\$[/tex] 20,000[tex]$ & $[/tex]\[tex]$ 13,910$[/tex] & [tex]$\$[/tex] 18,000[tex]$ & $[/tex]\[tex]$ 19,200$[/tex] \\
\hline
recurring debt & [tex]$\$[/tex] 310[tex]$ & $[/tex]\[tex]$ 198$[/tex] & [tex]$\$[/tex] 265[tex]$ & $[/tex]\[tex]$ 400$[/tex] \\
\hline
\end{tabular}

a. Person A

b. Person B

c. Person C

d. Person D



Answer :

To determine the person with the highest eligibility for a home loan, let's analyze each person's data based on the provided constraints. The lender requires a 15% down payment and evaluates eligibility based on the debt-to-income ratio.

1. Calculate the down payment for each person.

The down payment rate is 15% of the home value.

- Person A: [tex]\( \$95,000 \times 0.15 = \$14,250 \)[/tex]
- Person B: [tex]\( \$107,000 \times 0.15 = \$16,050 \)[/tex]
- Person C: [tex]\( \$120,000 \times 0.15 = \$18,000 \)[/tex]
- Person D: [tex]\( \$128,000 \times 0.15 = \$19,200 \)[/tex]

2. Check if each person's savings cover the required down payment.

A person is eligible if their savings are at least as much as the required down payment.

- Person A: Savings [tex]\( \$20,000 \)[/tex] which is more than the down payment [tex]\( \$14,250 \)[/tex]. Eligible.
- Person B: Savings [tex]\( \$13,910 \)[/tex] which is less than the down payment [tex]\( \$16,050 \)[/tex]. Not eligible.
- Person C: Savings [tex]\( \$18,000 \)[/tex] which is exactly the same as the down payment [tex]\( \$18,000 \)[/tex]. Eligible.
- Person D: Savings [tex]\( \$19,200 \)[/tex] which is equal to the down payment [tex]\( \$19,200 \)[/tex]. Eligible.

3. Calculate the monthly income and monthly debt payments.

We need to see how much each person can afford monthly based on their income and existing debt.

- Person A: Monthly income = [tex]\( \frac{\$46,000}{12} = \$3,833.33 \)[/tex]
Monthly debt = [tex]\( \$310 \)[/tex]
- Person B: Not eligible.
- Person C: Monthly income = [tex]\( \frac{\$58,000}{12} = \$4,833.33 \)[/tex]
Monthly debt = [tex]\( \$265 \)[/tex]
- Person D: Monthly income = [tex]\( \frac{\$60,000}{12} = \$5,000 \)[/tex]
Monthly debt = [tex]\( \$400 \)[/tex]

4. Calculate the maximum allowable housing expense based on the debt-to-income ratio.

The standard debt-to-income ratio is 36%.

- Person A: [tex]\( 0.36 \times 3,833.33 = \$1,380.00 \)[/tex] can be spent on housing (including the new loan).
- Person C: [tex]\( 0.36 \times 4,833.33 = \$1,740.00 \)[/tex] can be spent on housing (including the new loan).
- Person D: [tex]\( 0.36 \times 5,000 = \$1,800.00 \)[/tex] can be spent on housing (including the new loan).

5. Calculate the eligibility score.

The eligibility score is the maximum allowable housing expense minus the existing monthly debt.

- Person A: [tex]\( \$1,380.00 - \$310 = \$1,070.00 \)[/tex]
- Person C: [tex]\( \$1,740.00 - \$265 = \$1,475.00 \)[/tex]
- Person D: [tex]\( \$1,800.00 - \$400 = \$1,400.00 \)[/tex]

Based on the calculations:

- Person A's eligibility score is [tex]\( \$1,070.00 \)[/tex].
- Person C's eligibility score is [tex]\( \$1,475.00 \)[/tex].
- Person D's eligibility score is [tex]\( \$1,400.00 \)[/tex].

Thus, Person C has the highest eligibility score.

Therefore, the person that the lender would rate the highest on their eligibility for a home loan is Person C.

Answer: c. Person C