Natalie purchases a new car for $26,868. She pays 3,000 up front and agrees to make a $430 payment every month for 60 month

Natalie's car loses value as it get older. A common accounting method to track this loss of the value is straight-line depreciation. According to straight-line depreciation, Natalie's car loses $223 in value each month

After how many months will the money Natalie had paid equal the value of her car?

Question

Mathematics

Ozzy

20 December, 05:51

Natalie purchases a new car for $26,868. She pays 3,000 up front and agrees to make a $430 payment every month for 60 month

Natalie's car loses value as it get older. A common accounting method to track this loss of the value is straight-line depreciation. According to straight-line depreciation, Natalie's car loses $223 in value each month

After how many months will the money Natalie had paid equal the value of her car?

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Answers (1)

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Kristin Rowland · Answer 1

It will take 36.6 or 37 months.

We will set up an equation to represent this. Let m be the number of months. The amount of money she has paid can be represented by 3000+430m. The amount of money her car is worth can be represented by 26868-223m. Set these equal:

3000+430m=26868-223m

Add 223m to both sides:

3000+430m+223m = 26868-223m+223m

3000+653m=26868

Subtract 3000 from both sides:

3000+653m-3000 = 26868-3000

653m=23868

Divide both sides by 653:

653m/653 = 23868/653

m = 36.6