Question

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.

Answer 1

11.87 ~ 11.9years

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

Answer 2

`11.9\ years`

Explanation:

we know that

The formula to calculate the depreciated value is equal to

`V=P(1-r)^(x)`

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

`P=\$300,000\\r=14\%=14/100=0.14\\V=\$50,000`

substitute the values and solve for x

`50,000=300,000(1-0.14)^(x)`

`(50,000/300,000)=(0.86)^(x)`

`(5/30)=(0.86)^(x)`

Apply log both sides

`log(5/30)=(x)log(0.86)`

`x=log(5/30)/log(0.86)`

`x=11.9\ years`