A machine worth $ 11000 new and having a scrap value of $ 10995.6 is to be depreciated over a 4.4 -year life.
Find the function that describes straight line depreciation for this situation. At what time will the machine be worth $ 10997.8 according to this model?
So I know that the straight line depreciation is A(t) = -4.4t + 11,000. Is the machine worth $10997.8 when t = 0.5 years? That's what I keep on getting, but the other website keeps on saying it's wrong...
We want to find when it has depreciated by only $2.20? That does not seem like a reasonable question.
Must be that if it's worth $11000 new and has a scrap (fully depreciated value of $10995.6, we are only depreciating $5.40. Seems weird.
In any case, if that's true, then
A(t) = 11000 - (11000-10995.60)*t/4.4
to find when A = 10997.8, we just solve for t to get t=2.2 years.
Somehow the numbers don't make sense to have such a small depreciable value on such a large asset.
Of course, I could be all wrong.
Wait, Steve, I think that what you wrote:
A(t) = 11000 - (11000-10995.60)*t/4.4
is equivalent to what I wrote:
A(t) = -4.4t + 11,000
but when I solve mine, why do I keep on getting 0.5 instead of 2.2?
I'm dividing by 4.4 - you are multiplying.
As t goes from 0 to 4.4 years, the depreciation goes from 0 to the full amount.
Oh, ok, so it's not equivalent.
I get it now. It is 2.2. Thanks!
An easy way to check is to note that the $2.20 is half of the $4.40 being depreciated, so it took half of the depreciation period of 4.4 years: 2.2 years.
Odd that the asset life is the same as the amount being depreciated. Bad example, imho.
To find the function that describes straight line depreciation, we need to determine the rate at which the machine depreciates over time. In this case, the machine's value decreases from $11,000 to $10,995.6 over a period of 4.4 years.
To calculate the depreciation rate per year, we subtract the machine's scrap value from its initial value, and divide it by the machine's useful life:
Depreciation rate per year = (Initial value - Scrap value) / Useful life
= ($11,000 - $10,995.6) / 4.4
= $4.4 / 4.4
= $1
Therefore, the machine depreciates at a rate of $1 per year.
Now that we have the depreciation rate, we can determine the function that describes straight line depreciation for this situation. Let A(t) represent the value of the machine at time t.
A(t) = Initial value - (Depreciation rate per year * t)
A(t) = $11,000 - ($1 * t)
A(t) = $11,000 - t
So, the correct function that describes straight line depreciation for this situation is A(t) = $11,000 - t.
Now, let's find when the machine will be worth $10,997.8 according to this model.
A(t) = $10,997.8
$11,000 - t = $10,997.8
t = $11,000 - $10,997.8
t = 0.2 years
Therefore, according to this model, the machine will be worth $10,997.8 after 0.2 years.