Warner Cable Company needs to replace 5 vehicles. It considering 2 different types: Type HC with a higher cost and higher gas mileage and Type LC with a lower cost and lower gas mileage. Vehicle HC is $35000 and Vehicle LC is $28000. HC averages 43 miles per gallon of gas and LC averages 25. Warner plans to finance the vehicles over 4 years and they should last 8 years. The resale value of the vehicles is 10% of the original price. The average cost per gallon of gas over the 8 year period if $4.20 and each vehicle is driven the same number of miles over the 8 years.

1. What is the monthly payment for each type of vehicle (use interest rate of 6%)?
2. What is the total purchase cost for each type of vehicle?
3. What is the estimated fuel cost if each vehicle is driven 5000 miles annually?
4. What is the estimated fuel cost if each vehicle is driven 30000 annually?
5. Which vehicle type should Warner purchase? Justify your answer.
6. Summarize this scenario.

To answer the questions, we need to calculate the monthly payment, total purchase cost, and estimated fuel cost for each type of vehicle.

1. To calculate the monthly payment, we can use the formula for calculating a fixed monthly payment on a loan:

Monthly Payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:
P = Principal (loan amount)
r = Monthly interest rate
n = Number of months

For Type HC with a cost of $35,000, let's calculate the monthly payment:
Principal (P) = $35,000
Annual interest rate = 6%
Monthly interest rate (r) = Annual rate / 12 months = 6% / 12 = 0.5%
Number of months (n) = 4 years * 12 months = 48

Plugging the values into the formula:
Monthly Payment for Type HC = $35,000 * (0.005 * (1 + 0.005)^48) / ((1 + 0.005)^48 - 1)

Similarly, we can calculate the monthly payment for Type LC with a cost of $28,000.

2. The total purchase cost for each type of vehicle can be calculated by summing up the initial cost of the vehicle and the resale value after 8 years. The resale value is 10% of the original price.

Total purchase cost for Type HC = $35,000 + (10% * $35,000)
Total purchase cost for Type LC = $28,000 + (10% * $28,000)

3. The estimated fuel cost if each vehicle is driven 5000 miles annually can be calculated by multiplying the number of gallons used per year by the average cost per gallon.

Number of gallons used per year for Type HC = (5000 miles / 43 miles per gallon)
Estimated fuel cost for Type HC = Number of gallons * Cost per gallon

Similarly, we can calculate the estimated fuel cost for Type LC.

4. The estimated fuel cost if each vehicle is driven 30000 miles annually can be calculated in the same way as in question 3.

5. To determine which vehicle type Warner should purchase, compare the total purchase cost (including monthly payment and estimated fuel cost) for both types over the 8-year period. Choose the type that has the lower total cost.

6. In this scenario, Warner Cable Company is considering replacing 5 vehicles. They have two options: Type HC with higher cost and higher gas mileage and Type LC with lower cost and lower gas mileage. The vehicles will be financed over 4 years and are expected to last 8 years. The resale value of the vehicles is 10% of the original price. The average cost per gallon of gas over the 8-year period is $4.20, and each vehicle is driven the same number of miles annually. The questions revolve around calculating the monthly payment, total purchase cost, and estimated fuel cost for each vehicle type, as well as determining which type to choose based on the total cost.