Thread: 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?

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

Originally Posted by biancadee

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

Hmmm...all your posts are similar, Biancadee.
Sneaky way to get visitors to your homepage

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

anyway to do this without logs?

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

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

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...