Let's break down each individual's car purchase decision:
1) Joe's Decision
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Saving to Buy the Car:
- Joe saves $1,000 per month.
- To buy a $15,000 car, he will take: \[ \text{Months to save} = \frac{\text{Car Price}}{\text{Monthly Savings}} = \frac{15000}{1000} = 15 \text{ months} \]
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Discount for Cash Payment:
- Joe receives a 10% discount. The discount amount is: \[ \text{Discount} = 15,000 \times 0.10 = 1,500 \]
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Price After Discount:
- Therefore, the discounted price becomes: \[ \text{Discounted Price} = 15,000 - 1,500 = 13,500 \]
2) Marty's Decision
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Loan Payment:
- Marty takes out a loan for the full $15,000 and pays $500 per month for 3 years (36 months).
- Total amount paid by Marty over 3 years: \[ \text{Total Payment} = 500 \times 36 = 18,000 \]
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Interest Paid:
- The interest Marty pays is the total amount paid minus the car price: \[ \text{Interest} = \text{Total Payment} - \text{Loan Amount} = 18,000 - 15,000 = 3,000 \]
3) Sally's Decision
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Loan Payment:
- Sally already has $5,000 saved and needs to loan $10,000. She will pay $500 per month for 24 months.
- Total amount paid by Sally over 2 years: \[ \text{Total Payment} = 500 \times 24 = 12,000 \]
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Interest Paid:
- The interest Sally pays is the total amount paid minus the loan amount: \[ \text{Interest} = \text{Total Payment} - \text{Loan Amount} = 12,000 - 10,000 = 2,000 \]
Comparison
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Joe:
- Total Cost (after discount): $13,500
- No interest (paid in cash).
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Marty:
- Total Cost: $18,000
- Interest Paid: $3,000
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Sally:
- Total Cost: $12,000 (for the loan amount alone).
- Interest Paid: $2,000
Conclusion
When comparing these three scenarios:
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Best Decision: Joe made the best decision by paying cash. He had no interest costs and ended up paying only $13,500 for the car.
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Marty paid the most overall for the car ($18,000) due to interest costs, which is significantly more than the other two.
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Sally’s decision was better than Marty’s because she paid less overall ($12,000) and had lower interest costs, but Joe's decision remains the best in terms of savings.
Thus, Joe made the best decision in buying his car.