Question

Although appealing to more refined tastes, art as a collectible has not always performed so profitably. Assume that in 2015, an auction house sold a statute at auction for a price of $10,668,500. Unfortunately for the previous owner, he had purchased it in 2008 at a price of $12,700,500. What was his annual rate of return on this sculpture?

Answer 1

Answer:

-0.0246 or -2.46%

Explanation:

The duration 't' of his investment is:

$t= 2015-2008=7\ years$

The future value ($10,668,500) of an initial investment ($12,700,500) at a rate 'r' for a period of 7 years is given by:

$10,668,500=12,700,500*(1+r)^7\\1+r=\sqrt[7]{\frac{10,668,500}{12,700,500}}\\1+r=0.9754\\r=-0.0246=-2.46\%$

His annual rate of return was -0.0246 or -2.46%.

*A negative rate of return means that money was lost in this investment