A brand new music system is worth $18,000 in 2001. If the music system's value decreases by 6% every year, what will its value be in 2003?
2 Answers
Explanation:
You can use the formula:
Plug in:
(2 because 2003-2001 is 2).
Solve to get
Have a nice day!
The value of the music system in 2003 is
Explanation:
The function we will use is
A = P(1+r)^t
where
A= the final value of the music system
P= the initial value of the music system
r= the rate of growth per year
t= the number of years
(Since we're dealing with decay instead of growth,
To solve for
A=18000(1-0.06)^2
color(white)(A)=18000(0.94)^2
color(white)(A)=18000(0.8836)
color(white)(A)=15904.8
So the depreciated value of the music system is
Bonus:
Why does this formula work? Let's think of how much the music system would be worth after 1 year
A_1=0.94 xx 18000
The value of the music system after a 2nd year
A_2=0.94 xx A_1
color(white)(A_2)=0.94 xx 0.94 xx 18000
color(white)(A_2)=(0.94)^ 2 xx 18000
It's not hard to see that, if we extend this to a 3rd year, the value for
A=(1-r)^txxP