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Chapter 6: Problem 2

You are purchasing a new car. The price you negotiated with a car dealer in Staten Island, New York, was 17,944 dollars excluding sales tax. The sales tax rate for Staten Island is \(8.375 \%\). a. What growth factor is associated with the sales tax rate? b. Use the growth factor to determine the total cost of the car.

Short Answer

Expert verified
Answer: The total cost of the car, including sales tax, is $19,441.68.

Step by step solution

01

Calculate the growth factor for sales tax

To find the growth factor for the sales tax, we need to add the sales tax rate (expressed as a decimal) to 1. The sales tax rate is 8.375%. To convert this percentage to a decimal, we divide it by 100: \( \frac{8.375}{100} = 0.08375 \) Now, we add this decimal to 1: \( 1 + 0.08375 = 1.08375 \) So, the growth factor for the sales tax is 1.08375.
02

Calculate the total cost of the car

Now that we know the growth factor for the sales tax (1.08375), we can use it to find the total cost of the car. To do this, we'll multiply the negotiated car price by the growth factor. Price of the car: \(17,944\) Growth factor: \(1.08375\) Total cost of the car: \( 17,944 \times 1.08375 = 19,441.68 \) The total cost of the car, including sales tax, is $19,441.68.

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