Answer:
$15 827
Step-by-step explanation:
The formula for the amount A of depreciation of an asset by an annual percentage rate is
A = V(1 - r)ⁿ
where
n = number of years
r = annual percentage rate
V = value
Data:
n = 13 yr
r = 9 %
V = $22 400
Calculations:
A = 22 400(1 - 0.09)¹³ =22 400(0.91)¹³ = 22 400 × 0.293 45 = $ 6573
So, the car lost $6573 in value because of depreciation.
Current value = 22 400 - 6573 = $15 827
Answer:
The approximate value of the vehicle 13 years after purchase is $15827.
Step-by-step explanation:
The formula for the value lost of an asset after n years, with depreciation rate r(in decimal) is given by:
[tex]V = V_{0}(1-r)^{n}[/tex]
In which [tex]V_{0}[/tex] is the initial value.
In this problem, we have that:
A vehicle purchased for $22400 depreciates at a constant rate of 9%. This means that [tex]V_{0} = 22400[/tex] and [tex]r = 0.09[/tex].
Determine the approximate value of the vehicle 13 years after purchase.
This means that [tex]n = 13[/tex].
So
[tex]V = V_{0}(1-r)^{n}[/tex]
[tex]V = 22400*(0.91)^{13}[/tex]
[tex]V = 6573.34[/tex]
So, the approximate value of the vehicle 13 years after purchase is $22400 - $6573 = $15827.
