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Sagot :
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
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
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