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19 votes
19 votes
A new car is purchased for $18,000 and over time its value depreciates by one halfevery 6 years. What is the value of the car 19 years after it was purchased, to thenearest hundred dollars?

User Roy Van Rijn
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3.2k points

2 Answers

15 votes
15 votes

Answer: 2000

Explanation:

the answer is 2000 after rounding up 1999.9

17 votes
17 votes

We have the following:

We must pass the time from 19 years to periods of 6 years, as follows


(19)/(6)=3.17

That is, 19 years are 3.17 periods of 6 years

now, the formula to calculate the value of the car is


c=A\cdot(1-x)^n

Where A is the initial value, x is the depreciation and n is the time in periods of 6 years

Replacing:


c=18000\cdot(1-0.5)^(3.17)=1999.89

Therefore the value of the car would be approximately 1999.9 dollars

User James Irwin
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2.9k points