You have your eye on a nice, reliable used sedan after you are finished with school. You will probably only keep the car for 3 years before selling it. You and the dealer determine that you can either buy the $13,000 car (with 36 monthly payments) or lease it (for 36 months). If you buy it, you must make a down payment of $3,000 at n=0, and then you must pay off the balance in monthly installments based on a 1% effective monthly interest. You would plan to sell the car for $7,000 at the end of year 3. If you choose to lease the car, you must pay $1,500 at n=0 as an origination fee, and you will make 36 end-of-month lease payments of $250 each. At the end of the lease, you will return the car to the dealership. When considering the lease, use the same effective monthly interest rate as the buy option for determining equivalence. a. What will be the monthly payment amount if you choose the buy option? b. Which option is better (i.e., which option has the lowest equivalent cost)?

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### Understanding Car Financing Options: Buying vs. Leasing

You've found a reliable used sedan that you want to use post-graduation. Given that you'll likely keep the car for only three years before selling it, there are crucial financial decisions to be made. You have the option to either purchase the car directly or lease it. Let’s break down both scenarios:

1. **Buying the Car**:
    - **Initial Cost**: $13,000.
    - **Down Payment**: $3,000 at the start (t = 0).
    - **Monthly Installments**: The remaining balance will be paid in monthly installments for 36 months, based on an effective monthly interest rate of 1%.
    - **Selling the Car**: At the end of 3 years, it is assumed you will sell the car for $7,000.

2. **Leasing the Car**:
    - **Monthly Lease Payments**: You will make 36 end-of-month lease payments of $250 each.
    - **Origination Fee**: There is an additional one-time fee of $1,500.
    - **End-of-Lease**: After 36 months, you will return the car to the dealership.

#### Financial Assessments:
To make an informed decision, you need to calculate and compare the following:

**a. Monthly Payment Amount for Buying Option:**
   This involves determining the exact monthly installment you need to pay if you choose to buy the car.

**b. Cost Evaluation:**
   Assess which option (buying vs. leasing) is more financially viable in terms of the lowest equivalent cost.

### Additional Considerations:
- **Interest Rate Consistency**: For a fair comparison, the same effective monthly interest rate will be applied for both options.
- **Resale Value**: The potential resale value of the car at the end of 3 years is an important factor in the purchase option.

By evaluating these aspects, you can choose the most cost-effective method to finance your vehicle over the intended period of use.

---

This structured educational breakdown will help you navigate the financial intricacies of car ownership and leasing, assisting in making an informed and prudent decision.
Transcribed Image Text:### Understanding Car Financing Options: Buying vs. Leasing You've found a reliable used sedan that you want to use post-graduation. Given that you'll likely keep the car for only three years before selling it, there are crucial financial decisions to be made. You have the option to either purchase the car directly or lease it. Let’s break down both scenarios: 1. **Buying the Car**: - **Initial Cost**: $13,000. - **Down Payment**: $3,000 at the start (t = 0). - **Monthly Installments**: The remaining balance will be paid in monthly installments for 36 months, based on an effective monthly interest rate of 1%. - **Selling the Car**: At the end of 3 years, it is assumed you will sell the car for $7,000. 2. **Leasing the Car**: - **Monthly Lease Payments**: You will make 36 end-of-month lease payments of $250 each. - **Origination Fee**: There is an additional one-time fee of $1,500. - **End-of-Lease**: After 36 months, you will return the car to the dealership. #### Financial Assessments: To make an informed decision, you need to calculate and compare the following: **a. Monthly Payment Amount for Buying Option:** This involves determining the exact monthly installment you need to pay if you choose to buy the car. **b. Cost Evaluation:** Assess which option (buying vs. leasing) is more financially viable in terms of the lowest equivalent cost. ### Additional Considerations: - **Interest Rate Consistency**: For a fair comparison, the same effective monthly interest rate will be applied for both options. - **Resale Value**: The potential resale value of the car at the end of 3 years is an important factor in the purchase option. By evaluating these aspects, you can choose the most cost-effective method to finance your vehicle over the intended period of use. --- This structured educational breakdown will help you navigate the financial intricacies of car ownership and leasing, assisting in making an informed and prudent decision.
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