Question

Although appealing to more refined tastes, art as a collectible has not always performed so profitably. Assume that in 2015, an auction house sold a statute at auction for a price of $10,426,500. Unfortunately for the previous owner, he had purchased it in 2010 at a price of $12,662,500. 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.) Rate of return %

Answer 1

The annual rate of return on the sculpture is -17.63%.

Step-by-step explanation:

To calculate the annual rate of return on the sculpture, we need to determine the percentage change in its value from the purchase price to the selling price. The formula for calculating the rate of return is: Rate of return = ((Selling price - Purchase price) / Purchase price) * 100

Given that the purchase price of the sculpture in 2010 was $12,662,500 and it was sold in 2015 for $10,426,500, we can plug these values into the formula:

Rate of return = (($10,426,500 - $12,662,500) / $12,662,500) * 100

Simplifying the calculation gives us:

Rate of return = (-$2,236,000 / $12,662,500) * 100

Dividing the numerator and denominator, we get:

Rate of return = -0.1763 * 100

Rounding to 2 decimal places, the annual rate of return on the sculpture is -17.63%.

Answer 2

Answer: - 0.03811 or 3.81%

Step-by-step explanation:

Given that,

Selling price of statute(ending value) = $10,426,500

Purchasing Cost of statute (beginning value) = $12,662,500

n = 5 years

`Compound\ annual\ growth\ rate = ((Ending\ Value)/(Beginning\ Value)) ^{(1)/(n) } -1`

`Compound\ annual\ growth\ rate = ((10,426,500)/(12,662,500)) ^{(1)/(5)} -1`

= 0.9618 - 1

= - 0.03811 or - 3.81%