Question

Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, Sotheby’s sold the Edgar Degas bronze sculpture Petite Danseuse de Quatorze Ans at auction for a price of $10,311,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,377,500. 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:

His annual rate of return on this sculpture is -4.46%.

Explanation:

let PV be the amount invested and after t periods it turns to be FV

FV = PV(1+r)^t

(1+r)^t = FV/PV

1 + r = (FV/PV)^(1/t)

r = (FV/PV)^(1/t) - 1

t is the number of years from 1999 to 2003, t = 2003 - 1999 = 4 years

FV = $10,311,500

PV = $12,377,500

  r = ($10,311,500/$12,377,500)^(1/4) - 1

  r = -0.0446

therefore, His annual rate of return on this sculpture is -4.46%.