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A construction company purchased some equipment costing $300,000. The value of the equipment depreciates
(decreases) at a rate of 14% per year.
d. Estimate when the equipment will have a value of $50,000.

Respuesta :

calculista

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]  

samueladesida43

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