A computer is depreciated over 3 years.It costs $2300 and has an estimated scrap value of $200.The straight-line method is used for the first year.For the last two years,the constant percentage method is used,with depreciation rate d.In order to depreciate the computer from $2300 to $200 by the end of 3 years,what value of d is needed?

Question

Quizplus · Accepted Answer

Using the straight-line method for the first year, the depreciation amount is:

($2300 - $200) / 3 = $700 per year

After the first year, the remaining value of the computer is:

$2300 - $700 = $1600

Using the constant percentage method, we have:

Year 2: $1600 - d($1600) = $(1600 - 1600d)
Year 3: $(1600 - 1600d) - d($(1600 - 1600d)) = $200

Simplifying the equation for year 3:

$(1600 - 1600d) - d(1600 - 1600d) = $200
1600d - d(1600d) = $1400
1600d(1-d) = $1400
d(1-d) = 0.875

Solving for d using the quadratic formula:

d = (1 ± √3)/2

We choose the positive root since the depreciation rate cannot be negative.

d = (1 + √3)/2

d ≈ 0.646 or 64.6%

Therefore, the answer is B.

A Computer Is Depreciated Over 3 Years