After deciding to buy a new car, you can either lease the car or purchase it on a three-year loan. The car you wish to buy costs $35,000. The dealer has a special leasing arrangement where you pay $99 today and $499 per month for the next three years. If you purchase the car, you will pay it off in monthly payments over the next three years at a 6 percent APR. You believe you will be able to sell the car for $23,000 in three years.

    
What break-even resale price in three years would make you indifferent between buying and leasing? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

To determine the break-even resale price, we need to compare the total cost of leasing the car to the total cost of purchasing the car. The break-even resale price is the resale value of the purchased car in three years that makes the total cost of buying equal to the total cost of leasing.

Here’s the breakdown of both scenarios:

### 1. **Leasing the car:**

- Initial payment: $99 today
- Monthly payment: $499 for the next 36 months
- Total cost of leasing:

\[
\text{Total leasing cost} = 99 + (499 \times 36)
\]

### 2. **Purchasing the car:**

- Loan amount: $35,000
- Loan period: 3 years (36 months)
- Annual interest rate (APR): 6%

The monthly payment for a loan is calculated using the formula for an amortizing loan:

\[
M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}
\]

where:
- $M$ is the monthly payment,
- $P$ is the loan principal (amount borrowed),
- $r$ is the monthly interest rate (APR divided by 12),
- $n$ is the number of months.

The total cost of purchasing the car includes the loan payments and the resale value after 3 years:

\[
\text{Total cost of purchasing} = \text{Total payments} - \text{Resale value}
\]

We’ll set the total costs equal to find the break-even resale price.

Let’s calculate this step by step.

The break-even resale price, which would make you indifferent between leasing and purchasing the car, is **$20,268.64**. This is the amount you would need to sell the car for in three years to have the same total cost as leasing.

Here’s a summary of the calculations:
- **Total leasing cost**: $18,063
- **Monthly payment for purchasing**: $1,064.77
- **Break-even resale price**: $20,268.64

Would you like to dive deeper into any part of this calculation?

Here are 5 related questions for further exploration:
1. How does the break-even price change if the APR increases to 8%?
2. What would the total cost be if you leased the car for 4 years instead?
3. How would changes in the car’s resale value impact the decision to lease or buy?
4. What if the lease had a down payment—how would that affect the break-even price?
5. How does a balloon payment at the end of the loan affect your purchasing decision?

**Tip:** When considering a car lease vs. purchase, always compare both the total payments and the estimated resale value.

After deciding to buy a new car, you can either lease the car or purchase it on a three-year loan. The car you wish to buy costs $35,000. The dealer has a special leasing arrangement where you pay $99 today and $499 per month for the next three years. If you purchase the car, you will pay it off in monthly payments over the next three years at a 6 percent APR. You believe you will be able to sell the car for $23,000 in three years. What break-even resale price in three years would make you indifferent between buying and leasing?

Find out the break-even resale price that would make you indifferent between leasing and buying a $35,000 car with a 6% APR. Compare leasing costs and monthly payments using amortization formulas, and calculate the resale value needed to equal the total leasing cost.

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