A machine worth $ 11000 new and having a scrap value of $ 10995.6 is to be depreciated over a 4.4 -year life.

Question

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...

Answer 1

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.

Answer 2

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?

Answer 3

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.

Answer 4

Oh, ok, so it's not equivalent.

I get it now. It is 2.2. Thanks!

Answer 5

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.