Question 1028744: Harper buys a car in 2007 for $20000. Each year,the car decreases in value by 18%. How much will the car be worth in 2012? round to the nearest cent.
What's the common ratio?
I got it as 0.18. Is that correct?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! wrong.
he buys the car for 20,000
each year the car decreases in value by 18%.
so next year the value of the car is 20,000 - .18*20,000.
factor out the common term of 20,000 and you get 20,000 * (1 - .18
simplify this to get 20,000 * .82.
your common factor will be .82.
the car is worth 20,000 in 2007
you want to know how much the car is worth in 2012.
2012 - 2007 = 5 years.
the formula for compound value is f = p * (1+r)^n
in your case, p = 20,000.
r = -.18
n = 5
the equation becomes f = 20,000 * (1 - .18)^5 which becomes:
f = 20,000 * .82^5 which becomes:
f = 7,414.796864
the car will be worth 7,414.796864 in 5 years.
you can do the yearly calculations and you'll get the same answer.
start with 20,000 in 2007.
in 2008, the value of the car is 20,000 - .18 * 20,000 = 16,400.
in 2009, the value of the car is 16,400 - .18 * 16,400 = 13,448.
in 2010, the value of the car is 13,448 - .18 * 13,448 = 11,027.36
in 2011, the value of the car is 11,027.36 - .18 * 11,027.36 = 9,042.44.
in 2012, the value of the car is 9,042.44 - .18 * 9,042.44 = 7414.80.
that's the same as the answer we got above after rounding to 2 decimal digits.
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