# Depreciation.

• Jun 1st 2010, 05:25 AM
Mukilab
Depreciation.
Each year a car depreciated by 9%. Calculate the number of years after which the value of the car is 47% of it's original value.

I'm aware of the compound interest formula but I don't know if it would be any use here or how to reverse it because I'm not looking for a precise number. Should I create a number such as x and try and somehow change the compound interest formula so it's inverse?
• Jun 1st 2010, 08:00 AM
Wilmer
Quote:

Originally Posted by Mukilab
Each year a car depreciated by 9%. Calculate the number of years after which the value of the car is 47% of it's original value.

i is negative, so: (1 + i)^n = (1 - .09)^n = .91^n

.91^n = .47
n = log(.47) / log(.91) = 8.005695...purty close to 8 years (Wink)
• Jun 2nd 2010, 04:06 AM
Wilmer
Quote:

That was very well presented! :) I am learning a lot here.

Sneaky way to get visitors to your homepage (Wondering)
• Jun 3rd 2010, 03:32 AM
Mukilab
Quote:

Originally Posted by Wilmer
i is negative, so: (1 + i)^n = (1 - .09)^n = .91^n

.91^n = .47
n = log(.47) / log(.91) = 8.005695...purty close to 8 years (Wink)

anyway to do this without logs?
• Jun 4th 2010, 06:15 AM
Mukilab
Bump. Still no closer to a clue and its been ages. Hope the admin doesn't mind me bumping this.
• Jun 4th 2010, 06:18 AM
e^(i*pi)
Quote:

Originally Posted by Mukilab
anyway to do this without logs?

No, you must use logarithms but I cannot imagine why you could not just use a calculator
• Jun 4th 2010, 07:29 AM
Wilmer
Quote:

Originally Posted by Mukilab
Bump. Still no closer to a clue and its been ages. Hope the admin doesn't mind me bumping this.

Well, to be blunt, your original post doesn't make much sense;
what's "reverse" and "inverse"?

Once more, to find the number of periods, logs ARE REQUIRED.

Finding the "value left" after a GIVEN period is a different story: (1 + i)^n
With i = -.09 and n = 8: (1 - .09)^8 = .91^8 = .47025...