6.11 Buying or Leasing a Car
Financing a purchase against signing a lease: monthly payments and interest cost, residual value and mileage terms, plus kinds of auto insurance.
12 exercises
6.11 Exercise 1
Nichole negotiates with her car dealership so that the price is $21,800. She needs to pay the 6.75% sales tax on the car. Other fees are $31.00 for title and registration, $1,000 in destination fees, and a documentation fee of $175. What is the total cost of Nichole’s car?
6.11 Exercise 3
Sophia negotiates a $19,800 price for her new car. The sales tax is 9.5% in her area, and the dealership charges her $300 in documentation fees. Her title, plates, and registration come to $321.50. The dealership adds to this a destination fee of $1,100. If she places a down payment of $5,000 on the car, what is the total she will finance for the car?
6.11 Exercise 5
In the following, calculate the monthly payment using the given total to be financed, the interest rate, and the term of the car loan.
- Total to be financed is $31,885, interest rate is 2.9%, for 5 years.
- Total to be financed is $22,778, interest rate is 4.5%, for 6 years.
6.11 Exercise 7
Calculate the monthly payment for the used car if the total to be financed is $16,990, the interest rate is 7.5%, and the loan term is 3 years.
6.11 Exercise 9
Donna wants to lease a Subaru Outback in Eden, New York. Find the total cost of obtaining her lease if there is no down payment, $175.00 in acquisition fees, a security deposit of $300.00, $350.00 in disposition fees, $102.50 in title and registration fees, and sales tax of $3,536.05.
6.11 Exercise 11
- The purchase price of a car is $25,000. Its residual price is $14,500. What is its monthly depreciation for a 36-month lease?
- The purchase price of a car is $30,000. Its residual price is $18,600. What is its monthly depreciation for a 24-month lease?
6.11 Exercise 13
- Find the annual percentage rate if the money factor is 0.00001875.
- Find the money factor if the APR is 6.25%.
6.11 Exercise 15
Calculate the lease payments for car with the following price, residual price, length of lease, and money factor or APR.
- Price is $28,344, residual price is $18,140.16, 24-month lease, money factor is 0.000025.
- Price is $22,500, residual price is $13,050, 36-month lease, APR is 7.5%.
6.11 Exercise 17
In the following, determine if a lease or purchase of a car is better.
- Joyce is concerned with large repairs and does not want to deal with them.
- Maurice prefers to drive newer cars.
6.11 Exercise 19
- Which component of insurance pays if you are in an accident with a motorist without insurance?
- Which component of insurance pays for the remaining principal owed on your car in the case of a total loss?
6.11 Exercise 21
If your car payment is $287.50 per month and your car insurance is $930 every 6 months, what is the cost of the car per month when accounting for the insurance?
6.11 Exercise 23
Estella needs to budget for her car maintenance. She expects to buy new tires each 4 years, which will cost her $480 to replace them all. Oil changes near her cost $49.99, and she believes she will get one every 4 months. Her inspection costs $15 per year. Wipers for her car cost $95 for all three and she anticipates changing them every year. She drives less than 30,000 miles per year, so she plan…
Adapted from Contemporary Mathematics © 2023 Rice University. Licensed under CC BY 4.0. Source: Contemporary Mathematics. Imported at revision fa7c1a1.