Question

Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2015, an auction house sold a painting for a price of $1,080,000. Unfortunately for the previous owner, he had purchased it three years earlier at a price of $1,660,000.
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

Answer: -13.35%

Explanation:

Based on the information given in the question, the annual rate of return on this painting will be calculated thus:

Sales price of painting = $1,080,000

Cost price of painting = $1,660,000

The sales Price formula is given as

= Cost price × (1 +r)³

1080000 = 1660000 × (1+r)³

1,080,000/1,660,000 = (1+r)³

0.65 = (1 + r)³

Annual rate of return r will now be:

= 0.6506^⅓ - 1

= -13.35%