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Sagot :
To determine the best financial option for Alex as he plans for college, let's break down his costs and methods of payment step by step.
### Step 1: Calculate Total Costs per Year
First, we add up Alex's yearly tuition and fees, and room and board:
- Tuition & Fees: \[tex]$10,100 - Room & Board: \$[/tex]11,750
So, the total cost per year is:
[tex]\[ 10,100 + 11,750 = 21,850 \text{ dollars} \][/tex]
### Step 2: Calculate Total Payments per Year
Next, we calculate the total amount Alex receives from his grants and scholarships, and his work-study job:
- Grants & Scholarships: \[tex]$12,500 - Work-Study: \$[/tex]8,000
So, the total payment per year is:
[tex]\[ 12,500 + 8,000 = 20,500 \text{ dollars} \][/tex]
### Step 3: Determine the Difference
We need to find out if Alex's payments cover his costs by calculating the difference between his total payments and total costs:
[tex]\[ 20,500 - 21,850 = -1,350 \text{ dollars} \][/tex]
This means Alex is short by \[tex]$1,350 every year. ### Step 4: Evaluate Loan Needs If Alex were to take out a student loan, he wants an extra \$[/tex]2,000 per year for additional expenses ("mad money"):
- Shortfall: \[tex]$1,350 - Extra money needed: \$[/tex]2,000
Total loan needed per year:
[tex]\[ 1,350 + 2,000 = 3,350 \text{ dollars} \][/tex]
### Step 5: Determine the Best Option
Considering the different scenarios:
1. He doesn't need extra money: This hypothetically would be the case if his scholarships and work-study completely covered his costs. Since they do not, this is not an option.
2. He could work each summer to earn the \[tex]$1,350 difference: This is possible. Alex could earn the shortfall over the summer, covering his annual gap. 3. He could wait a year to earn the difference: This option is not ideal because he risks losing his scholarships, which are essential to his ability to cover the cost. 4. He could take out a student loan for the difference plus extra \$[/tex]2,000 a year: Alex could borrow \[tex]$3,350 each year to cover the shortfall plus have extra money, but this will increase his debt. Given these options, the best and most financially prudent choice is: ### Option 2: He could work each summer to earn the \$[/tex]1,350 difference.
By working each summer, Alex can bridge the \$1,350 gap without incurring additional debt, which also allows him to keep his scholarships and continue his education without disruption. Therefore, this is the recommended strategy for Alex.
### Step 1: Calculate Total Costs per Year
First, we add up Alex's yearly tuition and fees, and room and board:
- Tuition & Fees: \[tex]$10,100 - Room & Board: \$[/tex]11,750
So, the total cost per year is:
[tex]\[ 10,100 + 11,750 = 21,850 \text{ dollars} \][/tex]
### Step 2: Calculate Total Payments per Year
Next, we calculate the total amount Alex receives from his grants and scholarships, and his work-study job:
- Grants & Scholarships: \[tex]$12,500 - Work-Study: \$[/tex]8,000
So, the total payment per year is:
[tex]\[ 12,500 + 8,000 = 20,500 \text{ dollars} \][/tex]
### Step 3: Determine the Difference
We need to find out if Alex's payments cover his costs by calculating the difference between his total payments and total costs:
[tex]\[ 20,500 - 21,850 = -1,350 \text{ dollars} \][/tex]
This means Alex is short by \[tex]$1,350 every year. ### Step 4: Evaluate Loan Needs If Alex were to take out a student loan, he wants an extra \$[/tex]2,000 per year for additional expenses ("mad money"):
- Shortfall: \[tex]$1,350 - Extra money needed: \$[/tex]2,000
Total loan needed per year:
[tex]\[ 1,350 + 2,000 = 3,350 \text{ dollars} \][/tex]
### Step 5: Determine the Best Option
Considering the different scenarios:
1. He doesn't need extra money: This hypothetically would be the case if his scholarships and work-study completely covered his costs. Since they do not, this is not an option.
2. He could work each summer to earn the \[tex]$1,350 difference: This is possible. Alex could earn the shortfall over the summer, covering his annual gap. 3. He could wait a year to earn the difference: This option is not ideal because he risks losing his scholarships, which are essential to his ability to cover the cost. 4. He could take out a student loan for the difference plus extra \$[/tex]2,000 a year: Alex could borrow \[tex]$3,350 each year to cover the shortfall plus have extra money, but this will increase his debt. Given these options, the best and most financially prudent choice is: ### Option 2: He could work each summer to earn the \$[/tex]1,350 difference.
By working each summer, Alex can bridge the \$1,350 gap without incurring additional debt, which also allows him to keep his scholarships and continue his education without disruption. Therefore, this is the recommended strategy for Alex.
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