Problem 8-9 Buying versus Leasing a Motor Vehicle [LO8-2]
Purchase Costs
Down payment	$ 2,400	 
Loan payment	$ 470	for 36 months
Estimated value at end of loan	$ 5,000	 
Opportunity cost interest rate	5	percent
Leasing Costs
Security deposit	$ 680	 
Lease payment	$ 440	for 36 months
End of lease charges	$ 870	 
Based on the costs listed in the table above, calculate the costs of buying and of leasing a motor vehicle.

Note: Round your answers to the nearest whole number.



To compare the costs of buying versus leasing the motor vehicle, we need to calculate the total cost of each option over the 36-month period.

### 1. **Buying Costs:**

The total cost of buying a vehicle includes:
1. **Down payment**
2. **Loan payments over 36 months**
3. **Opportunity cost** (the interest you could have earned on the down payment if it were invested)
4. **Less the estimated value of the vehicle at the end of the loan**

Let's break it down:

- **Down payment**: $2,400
- **Loan payments**: $470 per month for 36 months, so:
  \[
  \text{Total Loan Payments} = 470 \times 36 = 16,920 \, \text{USD}
  \]
- **Opportunity cost**: The down payment could have been invested at an interest rate of 5%. The opportunity cost over 3 years (36 months) is calculated as:
  \[
  \text{Opportunity Cost} = 2,400 \times 0.05 \times 3 = 360 \, \text{USD}
  \]
- **Estimated value at end of loan**: $5,000

So, the total buying cost is:
\[
\text{Total Buying Cost} = 2,400 + 16,920 + 360 - 5,000 = 14,680 \, \text{USD}
\]

### 2. **Leasing Costs:**

The total cost of leasing includes:
1. **Security deposit**
2. **Lease payments over 36 months**
3. **End of lease charges**

Let's break it down:

- **Security deposit**: $680
- **Lease payments**: $440 per month for 36 months, so:
  \[
  \text{Total Lease Payments} = 440 \times 36 = 15,840 \, \text{USD}
  \]
- **End of lease charges**: $870

So, the total leasing cost is:
\[
\text{Total Leasing Cost} = 680 + 15,840 + 870 = 17,390 \, \text{USD}
\]

### **Summary:**

- **Total Buying Cost**: $14,680
- **Total Leasing Cost**: $17,390

**Conclusion:**
Buying the vehicle is less expensive, with a total cost of $14,680 compared to leasing, which would cost $17,390 over the same period.

Would you like more details on any part of this calculation or have any questions?

### Further Exploration:

1. How does the opportunity cost impact the overall decision between buying and leasing?
2. What would the total cost be if the interest rate were different?
3. How would a higher or lower estimated value at the end of the loan affect the buying cost?
4. What happens if the lease payments or loan payments differ slightly? How does that influence the decision?
5. What would be the breakeven point where both buying and leasing would cost the same?

**Tip:** Always consider the opportunity cost when making financial decisions, as it reflects the true cost of capital.

Compare the costs of buying versus leasing a motor vehicle over a 36-month period. This analysis includes detailed calculations of purchase costs such as down payment, loan payments, opportunity cost, and estimated vehicle value at the end of the loan. Leasing costs cover security deposit, lease payments, and end-of-lease charges. Discover which option is more cost-effective based on these calculations.

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