Lesson 5.9 - Unit 5 Project _Activity Sheet_

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Lesson 5.9 - Unit 5 Project _Activity Sheet_ Powered By Docstoc
					** Please show all work on separate paper and attach – no credit will be given for solutions that are missing work **

             Accelerated Pre-Calculus                        Name: ____________________________
                                               Unit 5 Project                         Due Date: ____________
                                      Exponential and Logarithmic Functions

             This project will give you an opportunity to research different automobiles, choose your
             favorite, and apply the material we have learned about exponential equations to calculate
             the finances necessary to purchase it.
             First, use the internet to research a few different vehicles (new or used) that you are
             interested in purchasing (maximum price of $35,000). Once you have selected a vehicle
             that meets your personal preferences, complete the following table:

                                          Price: $____________________

                  Make: _______________         Model: _______________        Color: __________

             The car dealership will expect full payment at the time of purchase. However, you do not
             have enough money to pay for the full price of the vehicle. Therefore, it is necessary to
             borrow money from a bank. Essentially, the bank will buy the automobile for you by
             paying the dealer the full price. You will then be responsible for repaying the bank by
             making monthly payments.
             However, banks require an upfront payment from you (the buyer). This ensures that the
             bank will receive at least some of the money you borrowed in case you are unable to make
             future monthly payments for some reason – for example, if you lose your job.
             This amount that is paid at the start of the loan is called the down payment.
             In today’s financial market, it is typical to make a down payment at 20% of the price of the
             automobile. Calculate the down payment necessary D to purchase the vehicle you chose:

                                            D = $____________________

             To calculate the remaining amount that you need to borrow from the bank, subtract your
             down payment D from the original price of the vehicle. This is called your loan balance L.

                                            L = $ ___________________

             The loan balance L is the remaining amount of money that is necessary to borrow from the
             bank in order to pay the dealership in full. You are then responsible for repaying the bank
             this amount. In addition to the loan balance, banks charge an annual interest fee which
             increases the amount of money that you must repay – this is how the bank makes a profit.
             In other words, you are responsible for repaying the bank the amount of money that you
             borrowed plus additional interest fees for their service of lending you money.
             Monthly payments and total payments vary depending on the length of the loan and the
             interest rate offered by the bank. Both of these variables (length of the loan and interest
             rate) are agreed upon by you and the bank when you purchase your new vehicle. Your
             personal financial situation (income, savings, expenses) need to be factored into the decision
             when choosing the length and interest rate of a loan. You will examine three possible loans
             and determine which is the best fit for you.
                                                      Loan Balance:
            Accelerated Pre-Calculus         L = $ ___________________
                                                             Name: ____________________________
                                     (copy from the front page for easy reference)
                                               Unit 5 T for a loan
             The monthly payment M and total paymentProject balance L over t years at an
                                       Exponential and following formulas:
             interest rate r can be calculated using theLogarithmic Functions

                     rL                                                              rL             
          M 
              1  1  r 12t
                                         12
                                                                           T 
                                                                                1  1  r 12t
                                                                                                        ·t
                       12                                                              12           
M = monthly payment           L = loan balance                 T = total payment L = loan balance
t = length of loan (years)    r = interest rate (decimal)      t = length of loan (years) r = interest rate (decimal)
           Use the above formulas to complete the table for the loan offers from each bank. Write
           the filled-in formulas for M and T and show how you calculated I in the boxes of the
           table. Then, use a calculator to find the values of M, T, and I.
         Bank                       PNC Bank                      Wachovia                     TD Bank
 Length of the Loan (t)               5 years                       8 years                     10 years
   Interest Rate (r)                    5%                           6.5%                        7.75%
 Monthly Payment (M)
                              M = $_______________            M = $_______________            M = $_______________
  Total Payment at
Completion of Loan (T)        T = $_______________            T = $_______________            T = $_______________
     Interest Paid (I)
                              I = $_______________             I = $_______________           I = $_______________
            Compare the length of each loan offer with the accompanying interest rate. Consider the
            bank’s situation and explain why the shorter loan lengths have smaller interest rates.

            Explain the benefits of a 5-year loan compared to a 10-year loan.

            Explain the disadvantages of a 5-year loan compared to a 10-year loan.

             Identify the loan that you believe offers the best deal or is the best fit for you.
               Bank: ________________             Time: __________           Interest Rate: __________

 Monthly Payment M: $__________                  Total Payment T: $__________            Interest Paid I: $__________

             Explain why you chose this loan option.
        Complete the following chart for the bank offer that you chose:
        Accelerated Pre-Calculus                       Name: ____________________________

                                           L = 5 Project
                        Loan Balance Unit$____________________
                                Exponential and Logarithmic Functions
                        Length of Loan     t = _____ years
                        Interest Rate        r = ________
                        Monthly Payment M = $____________________

        Monthly payments are divided into two parts: one part is responsible for reducing the
        actual balance of money borrowed from the bank while the other part reduces the amount
        of interest owed to the bank.
        The amount v that is paid toward reduction of the loan balance is given by the formula:
                                           rL   r 
                                   v   M  1  
                                           12  12 
        The amount u that is paid toward reduction of the interest owed is given by the formula:
                                           rL   r 
                               u  M   M  1  
                                           12  12 
        Using the loan balance L, length of loan t, interest rate r, and monthly payment M from
        the table at the top of this sheet complete the following table. Use the above formulas to
        calculate the portion of monthly payments that go toward reducing the loan balance
        compared to the portion that reduces the owed interest for each year of the loan. Write the
        filled-in formulas for v and u. Then, use a calculator to find the values of v and u.
                          Amount Paid Toward Loan Balance            Amount Paid Toward Interest Owed
   Year of Loan
                                        (v)                                        (u)

   1st Year (t = 1)

                                v = $_______________                            u = $_______________

  2nd Year (t = 2)

                                v = $_______________                            u = $_______________

  3rd Year (t = 3)

                                v = $_______________                            u = $_______________

Final Year (t = ___ )

                                v = $_______________                            u = $_______________

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