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Mr. Williams bought a car worth $120,493. (Not Really.) The car depreciates at a rate 31.9% annually. What is the car worth after 4 years? 9 years?

 Apr 20, 2015

Best Answer 

 #5
avatar+981 
+5

Thanks :)

 Apr 20, 2015
 #1
avatar+60 
+5

31.9% = 0.319, so all you have to do is solve the equation 120,493 - (120,493 * 0.319^n), where n stands for the number of years. So...

 

120,493 - (120,493 * 0.319^4) = 119245.26 , so $119245.26 on the 4th year

120,493 - (120,493 * 0.319^9) = 120488.88 , so $120488.88 on the 9th year

(The answers where rounded to the nearest hundreth)

 Apr 20, 2015
 #2
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So this is an exponential decay problem which the formula is y=ab^x where x would be < 1 so this equation would be y=120,493 • .681^x. You would find get the a value by the  the initial value and the b value by subtracting 100 the percent that they give you.  So after 4 years you would have 17648.0765, after 9 years 3795.64708. 

 Apr 20, 2015
 #3
avatar+981 
+5

The depreciation of the car can be written as

Future value(FV) = Present Value(P)*(1-rate(i))^number of years(n), or

 

$$FV=P(1-i)^n$$

 

so for 4 years . . .

 

$$FV=120493\times(1-0.319)^4=25914.94$$

 

And for 9 years . . .

 

$$FV=120493\times(1-0.319)^9=3795.65$$

.
 Apr 20, 2015
 #4
avatar+99352 
+5

Great answer Zac :)

 

Zectico, if you think about the answers that you got you will see that they simpley do not makes sense.

e.g.   The car is worth more after 9 years than it was after 4.

 

Anon,  you started off good but then I don't know what you did :/

 

(I think i will give you latter 2  points for your efforts  :))

 Apr 20, 2015
 #5
avatar+981 
+5
Best Answer

Thanks :)

zacismyname Apr 20, 2015

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