Question 1138112: 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 months. Nathalie's car loses value as it gets older A common accounting method to track this loss of value is straight-line depreciation. According to straight-line depreciation, Nathalie's car loses $233 in value each month. After how many months will the money Natalie has paid equal the value of her car?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
x = number of months
she makes a payment every month of $430, so after x of those months, she has paid 430*x dollars on top of the $3000 she already paid up front. In total, she pays 430x+3000 dollars after x months have passed by. Let y = 430x+3000, so y is the total amount she has paid so far.
Let z be the value of the car after x months. We can say
z = 26868 - 233x
since the car's value starts at 26868 dollars and drops by 233 dollars each month
Set y and z equal to each other, perform substitution, and solve for x
y = z
430x+3000 = 26868 - 233x
430x+3000+233x = 26868 - 233x+233x ... add 233x to both sides
663x+3000 = 26868
663x+3000-3000 = 26868-3000 ..... subtract 3000 from both sides
663x = 23868
663x/633 = 23868/663 .... divide both sides by 663
x = 36
Answer: At the 36 month mark (aka 3 years), is when the total amount Natalie has paid will equal the car's value.
side note: plug x = 36 into either the equation for y and z to find that
y = 430*x+3000 = 430*36+3000 = 18,480
z = 26868 - 233*x = 26868 - 233*36 = 18,480
meaning she has paid $18,480 and the car's value is this amount as well when 36 months have passed by.
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