Question

Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, a sculpture was sold at auction for a price of $10,309,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,382,500. What was his annual rate of return on this sculpture?

Answer 1

Answer:

i = 4.68698 %   to five decimal places.

Step-by-step explanation:

Let

i = annual rate of return

t = number of years = 4

using the compound interest formula,

12382500 = 10309500 (1+i)^4

rearrange

(1+i)^4 = 12382500 / 10309500

take log on both sides,

4log(1+i) = log(12382500 / 10309500)

solve for i

log(1+i) = (1/4)log(12382500 / 10309500)

1+i = e^((1/4)log(12382500 / 10309500))

i = e^((1/4)log(12382500 / 10309500)) -1

i = 0.0468698287401117