To determine which person has the highest eligibility for a home loan, we need to consider both the down payment and the debt-to-income ratio for each person.
1. Calculate the 20% down payment for each home value:
- Person A: [tex]\( 20\% \times 175,000 = 35,000 \)[/tex]
- Person B: [tex]\( 20\% \times 200,000 = 40,000 \)[/tex]
- Person C: [tex]\( 20\% \times 220,000 = 44,000 \)[/tex]
- Person D: [tex]\( 20\% \times 250,000 = 50,000 \)[/tex]
Therefore, the down payments are:
- Person A: [tex]$35,000
- Person B: $[/tex]40,000
- Person C: [tex]$44,000
- Person D: $[/tex]50,000
2. Calculate the monthly income for each person:
- Person A: [tex]\( \frac{51,000}{12} = 4,250 \)[/tex]
- Person B: [tex]\( \frac{58,000}{12} \approx 4,833.33 \)[/tex]
- Person C: [tex]\( \frac{63,000}{12} = 5,250 \)[/tex]
- Person D: [tex]\( \frac{67,000}{12} \approx 5,583.33 \)[/tex]
3. Calculate the debt-to-income ratio for each person:
Debt-to-income ratio is calculated as:
[tex]\[
\frac{\text{Monthly Recurring Debt}}{\text{Monthly Income}} \times 100
\][/tex]
- Person A: [tex]\( \frac{350}{4,250} \times 100 \approx 8.24\% \)[/tex]
- Person B: [tex]\( \frac{250}{4,833.33} \times 100 \approx 5.17\% \)[/tex]
- Person C: [tex]\( \frac{200}{5,250} \times 100 \approx 3.81\% \)[/tex]
- Person D: [tex]\( \frac{450}{5,583.33} \times 100 \approx 8.06\% \)[/tex]
4. Identify the person with the lowest debt-to-income ratio:
The debt-to-income ratios are:
- Person A: 8.24%
- Person B: 5.17%
- Person C: 3.81%
- Person D: 8.06%
Therefore, the person with the lowest debt-to-income ratio is Person C with a ratio of approximately 3.81%.
Based on the calculations, Person C should be rated the highest on their eligibility for a home loan.
The correct answer is:
c. Person C
