Respuesta :
Answer:
14.6328% , $5836.03
Step-by-step explanation:
Here we are going to use the formula
[tex]A_{0}(1-r)^n = A_{n}[/tex]
[tex]A_{0}[/tex] = 39000
r=?
[tex]A_{8}[/tex] = 11000
n=8
Hence
[tex]39000(1-r)^8 = 11000[/tex]
[tex](1-r)^8 = \frac{11000}{39000}[/tex]
[tex](1-r)^8 = 0.2820[/tex]
[tex](1-r) = 0.2820^{\frac{1}{8}[/tex]
[tex](1-r) = 0.2820^{0.125}[/tex]
[tex](1-r) = 0.8536[/tex]
[tex](1-0.8536=r[/tex]
[tex]r = 0.1463[/tex]
Hence r= 0.1463
In percentage form r = 14.63%
Now let us see calculate the value of car in 2003 that is after 12 years
we use the main formula again
[tex]A_{0}(1-r)^n = A_{n}[/tex]
[tex]A_{0}[/tex] = 39000
r=0.1463
[tex]A_{12}[/tex] = ?
n=12
[tex]39000(1-0.14634)^{(12} = A_{12}[/tex]
[tex]39000(0.8536)^{12} = A_{12}[/tex]
[tex]39000*0.1497 = A_{12}[/tex]
[tex]A_{12}=5840.34[/tex]
Hence the car's value will be depreciated to $5840.34 (approx) by 2003.
The annual rate of change between 1995 and 2003 is -0.1463
The annual rate of change between 1995 and 2003 is -14.63%
The value of the car in 2007 would be $5,844.24
The value of the car decreases as the years go by. This is referred to as depreciation. Depreciation is the decline in value of an asset as a result of wear and tear.
In order to determine the annual rate of change, use this formula:
g = [tex](FV / PV) ^{\frac{1}{n} } - 1[/tex]
Where:
g = depreciation rate
FV = value of the car in 2003 = $11,000
PV = value of the car in 1995 = $39,000
n = number of years = 2003 - 1995 = 8
[tex](11,000 / 39,00)^{\frac{1}{8} } - 1[/tex] = -0.1463 = -14.63%
The value of car in 7 years can be determined using this formula:
FV = P (1 + g)^n
$39,000 x (1 - 0.1463)^12
$39,000 x 0.8537^12 = $5,844.24
A similar question was answered here: https://brainly.com/question/12980665?referrer=searchResults
