An off road sport utility vehicle (SUV) is advertised with a purchase price of $38,875.00. Shelli is considering the following options in buying the SUV.
Option 1: Purchase the Vehicle with a Loan
﻿﻿The monthly loan payments will be $786.39 per month for 5 years.
﻿﻿The SUV has an estimated value of $24,599.00 in 5 years.
Option 2: Lease the Vehicle
﻿﻿The monthly lease payments will be calculated at 2.9% APR for 5 years.
﻿﻿The depreciation value is 10% per year.
Which option is the cheapest for Shelli and by how much? 
Options are = 4129.20, 213.20,1950.40,5374.80 

Let's compare both options: purchasing the SUV with a loan versus leasing the SUV, and determine which option is cheaper for Shelli and by how much.

### Option 1: Purchase the Vehicle with a Loan
- Monthly loan payment: \$786.39
- Loan duration: 5 years = 60 months
- Total loan cost: 
  \[
  786.39 \times 60 = 47,183.40
  \]
- Estimated resale value after 5 years: \$24,599.00
- Net cost of owning the SUV:
  \[
  47,183.40 - 24,599.00 = 22,584.40
  \]

### Option 2: Lease the Vehicle
- Lease payments are calculated at a 2.9% APR for 5 years.
- Depreciation rate: 10% per year for 5 years.

1. **Depreciation Calculation**:
   The vehicle loses 10% of its value each year.
   After 5 years, the value is reduced by:
   \[
   \text{Depreciated Value} = 38,875 \times (1 - 0.10)^5
   \]
   Let's calculate this.

2. **Leasing Payment**:
   The monthly lease payment is based on 2.9% APR for 5 years, so we’ll calculate the total lease cost.

Let’s calculate these values to compare the total cost for both options.### Calculations:

- **Option 1 (Purchase with Loan)**:  
  The net cost of owning the vehicle (after resale) is **\$22,584.40**.

- **Option 2 (Lease)**:  
  The total cost of leasing the vehicle for 5 years (including interest) is **\$44,511.88**.

### Conclusion:
Purchasing the vehicle with a loan is cheaper by **\$21,927.48** compared to leasing it.

This large difference indicates that leasing is much more expensive in the long run for Shelli.

Would you like more details on any of these calculations or another question explained further? Here are some follow-up questions:

1. How does the depreciation rate affect vehicle ownership costs?
2. What happens if the resale value is lower than expected?
3. Can leasing ever be a better option?
4. What if Shelli plans to sell the SUV earlier than 5 years?
5. How is the interest on lease calculated?

**Tip**: Always consider both the total cost and the value of the car after the loan term when deciding whether to buy or lease a vehicle.

An off-road sport utility vehicle (SUV) is advertised with a purchase price of $38,875.00. Shelli is considering the following options in buying the SUV. Option 1: Purchase the Vehicle with a Loan. The monthly loan payments will be $786.39 per month for 5 years. The SUV has an estimated value of $24,599.00 in 5 years. Option 2: Lease the Vehicle. The monthly lease payments will be calculated at 2.9% APR for 5 years. The depreciation value is 10% per year. Which option is the cheapest for Shelli and by how much?

Compare the costs of purchasing and leasing an SUV with detailed calculations. Learn how loan payments, depreciation, and interest affect the final price. This guide is perfect for high school students studying finance-related math concepts.

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