Question

An car was purchased for $47000 and its depreciation value is 22% each year.

How long would it take the car to be worth nothing (zero dollars)?
Explain.

Answer 1

since it decreases by 22% each year, 78% of the previous years value will be maintained.
so you have

Value = 47000(.78)^n where n is the number of years.

so for the value to be zero dollars, we could set Value = 0 and solve for n

this causes a problem, since to solve
0 = 47000(.78)^n
n = log 0/log.78 , but log 0 is undefined, implying that n would be infinitely large

this makes sense, since as long as I have any amount left, 78% of it will still be some value

If I decide that a value of 49 cents is less than a Dollar, if we round to the nearest dollar, I get

.49 = 47000(.78)^n
I get n = appr. 46 years.