SOLUTION: George buys a car for $25 000 in January 2017. If the car depreciates at a rate of 12.5% per annum, (a) Write down an equation that represents the value of the car, defining clear

Question 1098873: George buys a car for $25 000 in January 2017. If the car depreciates at a rate of 12.5% per annum,
(a) Write down an equation that represents the value of the car, defining clearly any variables you use.
(b) How much will the car be worth in January 2023.
(c) How long will it take for the car to depreciate to $5000.
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
(a)The future value of the car would be:
FV=25,000*(1-0.125)^y where FV is the future value of the car, and y is the number of years since January, 2017.
(b)2023-2017=6
FV(2023)=25,000*(0.875)^6=$11219.88 as the value of the car in the year 2023
(c)5000=25,000*(0.875)^y
.2=0.875^y
ln 0.2=ln 0.875^y=y ln 0.875
y=ln 0.2/ln 0.875=12.053 years
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