Question

Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, an auction house sold a sculpture at auction for a price of $10,361,500. Unfortunately for the previous owner, he had purchased it in 2000 at a price of $12,477,500. What was his annual rate of return on this sculpture?

Answer 1

Answer:

-0.06 or -6%

Explanation:

The duration 't' of his investment is determined by subtracting the selling year by the purchasing year:

$t = 2003-200 = 3\ years$

The future value ($10,361,500) of this original investment ($12,700,500) at a rate 'r' for a period of 3 years is given by:

$10,361,500=12,477,500*(1+r)^3\\r=\sqrt[3]{\frac{10,361,500}{12,477,500}} -1\\r=-0.06$

His annual rate of return was -0.06 or -6%.

*Since he had a negative rate of return, the previous owner lost money in this investment