Question

Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2010, Deutscher-Menzies sold Arkie under the Shower, a painting by renowned Australian painter Brett Whiteley, at auction for a price of $1,100,000. Unfortunately for the previous owner, he had purchased it three years earlier at a price of $1,680,000. What was his annual rate of return on this painting?

Answer 1

the annual rate of return on the painting was -13.17%

Step-by-step explanation:

we will construct the equation for future value at the annual rate of return at which a principal of 1,680,000 return 1,100,000 in three years:

`Principal \: (1+ r)^(time) = Amount`

Principal 1,680,000

time 3 years

Amount 1,100,000

rate r

`1,680,000 \: (1+ r)^(3) = 1,100,000`

`r = \sqrt[3]{ 1,100,000 / 1,680,000} -1`

r = -0.131650681 = -13.17%

As expected, because the amount after three years is lower than the principa the rate of return is negative