Straight-line depreciation is an accounting method used to help spread the cost of new equipment over a number of years. It takes into account both the cost when new and the salvage value, which is the value of the equipment at the time it gets replaced. The function where V is value and t is time in years, can be used to find the value of a large copy machine during the first 7 years of use. After how many years will the copier be worth only $6,000? Round your answer to the nearest hundredth.
A) 4.62 years
B) 7.00 years
C) 5.59 years
D) 6.12 years
E) 6.93 years

Question

Straight-line depreciation is an accounting method used to help spread the cost of new equipment over a number of years. It takes into account both the cost when new and the salvage value, which is the value of the equipment at the time it gets replaced. The function  where V is value and t is time in years, can be used to find the value of a large copy machine during the first 7 years of use. After how many years will the copier be worth only $6,000? Round your answer to the nearest hundredth. 
A) 4.62 years 
B) 7.00 years 
C) 5.59 years 
D) 6.12 years 
E) 6.93 years

Quizplus · Accepted Answer

We need to solve the equation with V = $6,000 to find the value of t:

V = (C - S) x (1 - r)^t + S

$6,000 = ($16,000 - $2,000) x (1 - 0.25)^t + $2,000

$6,000 - $2,000 = $14,000 x 0.75^t

$4,000 = $14,000 x 0.75^t

0.75^t = 0.286

t = log(0.286)/log(0.75) ≈ 5.59 years

Therefore, the copier will be worth only $6,000 after 5.59 years of use. The closest answer choice is C) 5.59 years.

Straight-Line Depreciation Is an Accounting Method Used to Help Spread