Calculating Rates of Return [LO3] 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 $10,401,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,557,500.

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.) Annual rate of return

Question

Business

Emilie

15 August, 21:12

Calculating Rates of Return [LO3] 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 $10,401,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,557,500.

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.) Annual rate of return

+2

Answers (1)

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Sims · Answer 1

- 4.6%

Explanation:

Data provided in the question:

Future value of the sculpture = $10,401,500

Present value of the sculpture = $12,557,500

Time period, n = 2003 - 1999 = 4 years

Now,

We know,

Future value = Present value * (1 + r) ⁿ

here,

r is the annual rate of return

thus,

$10,401,500 = $12,557,500 * (1 + r) ⁴

or

(1 + r) ⁴ = 0.82831

or

1 + r = 0.954

or

r = 0.954 - 1

or

r = - 0.046

or

r = - 0.046 * 100%

= - 4.6%