A business purchases a computer system for $3000. If the value of the system decreases at a rate of 15% per year, how much is the computer worth after 4 years?

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- anonymous

- katieb

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- anonymous

you multiply by .85 repeatedly, so 3000*.85^4
.85 because 100% = 1.00 and 15% decrease = 1.00 - .15 = .85

- anonymous

Wait huh? :I

- anonymous

what part is confusing, I'll try to make it make sense...

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- anonymous

3000 * .85 = 2550 (after one year)
2550 * .85 = 2167.5 (after two years)
but look, 2550 = 3000*.85, so after the second year can be found by:
(3000*.85)*.85
which equals 3000*.85^2
so after 4 years, the exponent becomes a 4

- anonymous

Each year its value decrease by 15% of its original value. In 4 years, it will decrease by 4*15%=60%. That means it will cost just 40% of its original value. So, its value after 4 years is: (40/100)*3000=$1,200

- anonymous

No, the answer is not 1200

- anonymous

because it is not losing 15% of 3000 each year. the second year, you lose 15% of a smaller number.

- anonymous

OMG, Stick with tonks :)

- anonymous

By AnwarA's calculation, you would have no money after 8 years, but you can lose 15% for ever

- anonymous

Aha, I'm still trying to figure the problem out myself

- anonymous

Monie, does using .85 make sense?

- anonymous

Yea it does

- anonymous

okay, then do it out slowly instead of any shortcuts

- anonymous

But why .85?

- anonymous

oh,
if there were no change, you would have 100% the next year. Since there is a 15% decrease, you have 15% less than 100%, or 85% next year. Then move the decimal over to turn a percent into something you can multiply with for .85

- anonymous

I end up with 0.7225...Is that correct? .-.

- anonymous

hmmm,
3000*.85 = year 1
(3000*.85)*.85 = year 2
((3000*.85)*.85)*.85 = year 3
(((3000*.85)*.85)*.85)*.85 = year 4 = 3000*.85*.85*.85*.85 = ...

- anonymous

do you see why each step works?
What do you get?

- anonymous

I get 1556.01875....
But I'm guessing it to be 1556? Correct?

- anonymous

I think you should keep it to the penny, 1556.02

- anonymous

yes, do you get the .85 and the repeated multiplying?

- anonymous

Yes I do :). THank you so very much for helping me Tonks.

- anonymous

ur welcome

- anonymous

One more question if you don't mind? (:

- anonymous

If it is a math problem, post it as a new thread

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