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?
+60 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)
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.
+980 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 . . .
$$FV=120493\times(1-0.319)^9=3795.65$$
+118608 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 :))
