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- From: Mathematics, Algebra
- Posted on: Fri 31 Jan, 2014
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**Simple Interest Car Loan Linear Function**

A financial institution in your community is advertising “Simple Interest Car Loans.” Here is their ad:

"Looking for an attractive loan for the car of your dreams? Well, you have to look no more. Come in and show us your car deal. We will match any car loan and reduce the interest rate by **1%**, with our “simple interest car loan”. No down payment needed, and no trade-ins. Our loans must have a minimum interest rate of .5%."

In this assignment you are examining common applications of linear functions. Here, the linear function is F(r) = (pt)r + p, where *r* is the independent variable (the interest rate changes) and *F(r)* is the dependent variable (F(r) is the total cost of the car for different interest rates). For F(r) = (pt)r + p to be considered a linear function, the values of *p* (the sales price of the car) and *t* (the time in years for repaying the loan) must remain constant in the calculations.

1. Search the Internet and **locate the sale price** for the car of your dreams. (**For the purpose of this exercise, you can ignore sales, down payments, taxes, and other normal purchase expenses.) **This is *p* in this assignment.

2. Determine the annual interest rate for your loan using **information from a local bank or an internet ad and be sure to give your references**. Reduce this rate by **1%**. This is one value of r, but expressed as a decimal. The decimal equivalent of this interest rate is one of the values of* r* in this assignment.

3. Decide the time, in years, you wish to repay the loan (typically, 3-7 years, half years like 5.5 years are okay). This is* t* in this assignment.

4. Determine the interest on your loan, using the formula:

- Interest = sale price*time*rate, (I = ptr).

5. Determine the total cost of your loan, using the formula:

- Total cost = (sale price*time)rate + Sale Price

6. Model the total cost as a linear function, with interest rate as the independent variable:

- TC(r) = (pt)r + p.

7. Divide the total cost by the number of months, to determine the monthly payment.

8. Repeat steps 4, 5, 6, and 7 to determine the cost of the loan if the interest rate had not been reduced by 1% – how much money did you save monthly and in total?

9. Summarize your findings by writing a brief statement that includes the pertinent information from the steps above; rates, totals, savings, etc.

10. Include references formatted according to APA style.

11. Respond to a classmate’s posting. If you think there may be an error, feel free to help your classmate without providing the correct answer. Otherwise, analyze the post in comparison to yours or add new information to the discussion.

12. Assume that you have no more than $600 per month to spend for a car loan. Based on your experience with these calculations, is there any combination of your lower interest rate and number of years (up to 7 years) that you could afford at $600 per month that would give you a “good deal” for buying your dream car? Explain why or why not.

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