Answer:
[tex]11.9\ years[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]V=P(1-r)^{x}[/tex]
where
V is the depreciated value
P is the original value
r is the rate of depreciation in decimal
x is Number of Time Periods
in this problem we have
[tex]P=\$300,000\\r=14\%=14/100=0.14\\V=\$50,000[/tex]
substitute the values and solve for x
[tex]50,000=300,000(1-0.14)^{x}[/tex]
[tex](50,000/300,000)=(0.86)^{x}[/tex]
[tex](5/30)=(0.86)^{x}[/tex]
Apply log both sides
[tex]log(5/30)=(x)log(0.86)[/tex]
[tex]x=log(5/30)/log(0.86)[/tex]
[tex]x=11.9\ years[/tex]
Answer:
11.87 ~ 11.9years
Step-by-step explanation:
Formula for calculating depreciated value is:
A = P(1 - R/100)^n
Where A= Depreciated value of equipment after n years($50,000)
P = Initial cost of equipment($300,000)
R = Depreciated rate of equipment per annum (14%)
n = number of years (n)
Next, we insert the figures into the formula
50000 = 300000 (1 - 14/100)^n
Divide both sides by 300000
5/30 = (1- 14/100)^n
0.167 = (1 - 0.14)^n
0.167 = (0.86)^n
Add log to both sides
log 0.167 = (n)log 0.86
Divide both sides by log 0.86
n = log 0.167/log 0.86
n = 11.866
Therefore, it can be estimated that it will take approximately 11.9years for the initial cost to depreciate to $50,000
