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6 January, 17:25

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

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  1. 6 January, 17:43
    0
    - 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%
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