Brad bought $5,141 worth of office equipment. The government allows for office equipment to be depreciated at an annual rate of 5.5% per year. How long will it take for Brad to depreciate the equipment fifty-four percent?
100 - 5.5 = 94.5 so
present value = original value * .945^n
100 - 54 = 46
so final value = original value * .46
so
original value *.46 = original value * .945^n
or
.945^n = .46
n log .945 = log .46
n = log.46/log.945 = 13.7 years
My answer assumes depreciation per year is based on current depreciated value. If instead it is "straight line" or a constant amount per year then
.055 * original value = amount per year
.055 n = .54
n = 9.82
You problem does not specify which type of depreciation is intended.
To calculate the time it will take for the office equipment to depreciate by fifty-four percent, we need to first find the amount of depreciation that occurs each year.
The annual depreciation rate is 5.5%, which means the equipment value reduces by 5.5% each year. Therefore, the amount depreciated each year can be calculated as:
Depreciation per year = 5.5% of $5,141
Depreciation per year = (5.5/100) * $5,141
Depreciation per year = $282.755
To find the time it will take for the equipment to depreciate by fifty-four percent, we divide the depreciation amount by the annual depreciation.
Time (in years) to depreciate = Depreciation amount / Depreciation per year
Time (in years) to depreciate = 54% of $5,141 / $282.755
Time (in years) to depreciate = (54/100) * $5,141 / $282.755
Time (in years) to depreciate = $2776.14 / $282.755
Time (in years) to depreciate ≈ 9.818 years
Therefore, it will take approximately 9.818 years for the equipment to depreciate by fifty-four percent.
To find out how long it will take for Brad to depreciate the equipment by fifty-four percent, we need to calculate the depreciation amount each year until the total depreciation reaches fifty-four percent.
First, let's calculate the amount that needs to be depreciated. Fifty-four percent of $5,141 is:
$5,141 * 0.54 = $2,773.14
Now, let's determine the annual depreciation amount. The government allows for office equipment to be depreciated at an annual rate of 5.5%. So, the annual depreciation amount can be calculated as:
$5,141 * 0.055 = $282.75
Next, let's find out how many years it will take to reach a total depreciation of $2,773.14. We can use the following formula:
Number of years = Total depreciation amount / Annual depreciation amount
Number of years = $2,773.14 / $282.75
Rounding up to the nearest whole number, the number of years it will take for Brad to depreciate the equipment fifty-four percent is approximately 10 years.
Therefore, it will take Brad approximately 10 years to depreciate the office equipment by fifty-four percent.