Exponential Function Group Project

1) Part #1

At the reading of the will of your great aunt you find that she left you $10,000 to help you buy a house when you finish your education. However, your great aunt was very frugal. The will stipulates to receive the money you must find the bank in your town that gives you the highest interest and you cannot make any withdrawals for 7 years.

Contact three financial institutions by looking on the internet. Find the interest rate for a student savings or personal savings account. For this assignment, assume that the given interest rates are compounded 1) annually, 2) quarterly, 3) monthly and 4) daily. Use the table below to record your information (note: find banks with different interest rates):

Financial institution / Web address / Interest Rate
1
2
3

Based on the given information and the interest data you found answer the following.

1. Choose the bank which will give you the highest interest rate and write the mathematical model. ( 10points)

Bank Name: ______

Annually:Monthly:

Quarterly:Daily:

2. How much money will you have in the bank in 7 years?(10points)

Annually:Monthly:

Quarterly:Daily:

  1. When will your money double?(10points)

Annually:Monthly:

Quarterly:Daily:

This is part 1 of your group project. Turn in this sheet for part 1.

Each member will need to initial prior to turning this sheet in acknowledging they participated in this assignment and agree with these answers.

Group Members______

Exponential Function Group Project

Part #2

  1. You are going to buy a car that will need to be financed. You will need to look at different options and decide which will be the best choice for your situation. You will need to find a car on the internet that you want to purchase.We want to chose as car that has been in production for at least eight years.

Process

1. Find an advertisement for a car that you would like to purchase. You can look at any internet site, but you might consider: to learn how the advertised prices compare with market prices generally for cars of the same make, model and year.

Car Make ______Model ______

Year ______Miles ______Price __$______

2. Once you have found the automobile you want to purchase and determined how much you will be spending on the car, you need to calculate the monthly payments. There is a monthly payment calculator at which can help you calculate the monthly payments according the amount you will be borrowing, the interest rate, and the number of years you plan to make payments. Calculate the monthly payment for your car for each option given below. Use 6% sales tax.

Loan / Interest Rate / Length in Years / Monthly Payment / Actual Cost of Vehicle after Loan is Paid
1 / 5% / 5
2 / 7.5% / 3
3 / 9.99% / 4.5
4 / 11.5% / 2.5
5 / 18% / 4

3. Make a decision as to what you think is the best option and be able to justify your conclusion. Think about what situations might make you decide not to take each of the following:

  • Lowest interest rate
  • Smallest monthly payment
  • Shortest time
  • Loan with lowest cost

Exponential Function Group Project

Part #3

  1. Now that you have chosen your car, you will see how its value depreciates. Access the web site: and click on the hyper link “Private Party” as shown to the below.

USED CAR VALUES FOR SHOPPERS

Shopping for a used car? Check out Blue Book values before you buy. Choose Used Car Retail Value if you intend to buy from a dealer. Choose Private Party Value if you intend to buy from another consumer

To be consistent, determine the features you desire and use the same features for each year’s model, and use the default mileage given. Complete the table.

Vehicle: Condition:
Years Old
Year Made
Value
  1. Determine which variable is independent and which is dependent. Enter the data into lists on your calculator. Use Years Old and Value as variables.Create a scatter plot of the data and determine which function (linear, quadratic, or exponential) best models the data.
  1. Find the regression function. Identify what x and y represent.
  1. Discuss the goodness of fit of this model.
  1. What information does this model give us about the values of cars over time? What is the specific meaning of each constant in the model? What is a reasonable domain for the model? (Write in complete sentences.)
  1. What is the rate of growth or decay in the value of the vehicle?
  1. Predict the value of a 20-year-old vehicle.
  1. What year will the vehicle be nearly worthless (less than $100)?

Your Analysis should include the following

The model for this data is C(x)= $ a(b)x. What information is in this model?

  1. If then we know the value (what we could sell it for) is $______for a brand new Name of your car door in good condition.
  2. The base of the exponent is _____. This base tells us that as we move from one year’s model to the model of the previous year the value is multiplied by ______. The value is ______% of the value of a car one year newer.
  3. Usually with rates we turn that around and think about multiplying by which in this case would be

1- r= b or the value drops by r% with each year that goes by.

  1. Using this model we can predict the value of a 20-year-old Ford Taurus LX Sedan 4 door in good condition. In this case, $ a(b)20= value in 20 years.
  2. The car will be worth less than 100 in ___ years.

4. Your final report will be a poster including the following:

  • Part 1 - An ad for the car you chose to purchase make & model(with a picture) and price(10pts)
  • Part 2 – The completed table that shows the monthly payment and the total cost of the loan for each option. Also, copy and paste the loan summary and yearly amortization schedule from the loan calculator website.(10pts)
  • Part 3 – Your explanations to Part 2 #3. (they don’t have to be long, just explain each one)(10pts)
  • Part 4 - Summary of which is the best loan option for you along with a justification of why.(10pts)
  • Part 5 Depreciation data table and answers to Questions 2-8 (your analysis of the model) (20pts)
  • Part 6 - Summary of what you learned from this project. (10points)

Your final report should be organized with each part labeled and it should be easy for me to read.