Assume that the depreciation on a new car can be determined by the formula V=C(1-r)^t?

where Vis the value of the car after t years,Cis the original cost %26amp; r is the rate of depreciation.A car purchased 10 yrs ago , when it was new , now has a value of 6000$ . if the car's original cost was 24000$, what is the rate of depreciation

Assume that the depreciation on a new car can be determined by the formula V=C(1-r)^t?
V = 6000


C = 24000


t = 10





Plug them in and solve for r





6000 = 24000(1-r)^10





(1-r)^10 = 1/4





Take the 10th root of both sides





1-r = (1/4)^(1/10)





r = 1 - (1/4)^(1/10) = 0.129449437








So depreciation is about 12.94% per year.





I see you changed t=10 to t=6. Just do what I did above, only use 6 instead of 10 and you'll get the right answer. Do not worry if this does not reflect what real-world depreciation works like. It's only a math problem that you have to solve.
Reply:there is a flaw with you formula is that it is not steady depreciation. The car depreciates the most during the first year, then less the second, and so on. Also different models depreciate differently in different markets. There are also outside forces like 3 gal gas that affect depreciation. Unfortunatelly there is no set way to figure it out.

columbine