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 $10,291,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,337,500. What was his annual rate of return on this sculpture? (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:

r = (- 4.431%)

Explanation:

Given that,

During 2003, auction house sold a sculpture(Final value) = $10,291,500

Purchasing Price of sculpture in 1999(Initial value) = $12,337,500

No. of years elapsed = 2003 - 1999

                                   = 4 years

$Final\ value=Initial\ value(1+rate\ of\ return)^{No.\ of\ years}$

$10,291,500=12,337,500(1+r)^{4}$

$\frac{10,291,500}{12,337,500}=(1+r)^{4}$

$(0.834164134)^{\frac{1}{4} }=(1+r)$

0.955680838 - 1 = r

- 0.04431 = r

- 4.431% = r

Therefore, annual rate of return on this sculpture is -4.431%