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 3 years earlier at a price of $1,680,000. What was his annual rate of return on this painting? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

the interest rate will be negative: -13.17%

Step-by-step explanation:

annual rate of return:

Using the formula for future value of a lump sum and we can solve for rate:

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

Principal 1,680,000

time 3 years

Amount 1,100,000

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

`(1+ rate)^(3) = 1,100,000 / 1,680,000`

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

rate = -0.131650681 = -13.17%