Matt Wolf



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:

The car dealership will expect full payment at the time of purchase. However, you do not have enough money to pay 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 of 20% of the full price of the automobile. Calculate the down payment (D) necessary to purchase the vehicle you chose:

D = $____________________

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

L = $ ___________________

The loan balance 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.

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: __________ |

In today’s financial market, it is typical to make a down payment of 20% of the full price of the automobile. Calculate the down payment (D) necessary to purchase the vehicle you chose:

D = $____________________

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

L = $ ___________________

The monthly payment M and total payment T for a loan balance L over t years at an interest rate r can be calculated using the following formulas.

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.

The amount v that is paid toward reduction of the loan balance is given by the formula:

[pic]

The amount u that is paid toward reduction of the interest owed is given by the formula:

[pic]

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.

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|Price: $____________________ |

|Make: _______________ |Model: _______________ |Color: __________ |

Due Date: ____________

** Please show all work on separate paper and attach – no credit will be given for solutions that are missing work **

[pic]

M = monthly payment L = loan balance

t = length of loan (years) r = interest rate (decimal)

[pic]·t

T = total payment L = loan balance

t = length of loan (years) r = interest rate (decimal)

|Bank |PNC Bank |Wells Fargo |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 = $_______________ |

Identify the loan that is the best fit for you: Bank: ____________ t = _____ r = _____

Explain why you chose this loan option:

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

Complete the following chart for the bank offer that you chose:

|Loan Balance |L = $____________________ |

|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.

|Year of Loan |Amount Paid Toward Loan Balance |Amount Paid Toward Interest Owed |

| |(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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