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 $10,341,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,437,500.

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 $10,341,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,437,500.

  

What was his annual rate of return on this sculpture? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

 

Annual rate of return

%

Explanation:

We can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:

  

FV = PV(1 + r)t

Solving for r, we get:

r = (FV / PV)1 / t – 1

r = ($10,341,500 / $12,437,500)1/4 – 1 = – 4.51%

Notice that the interest rate is negative. This occurs when the FV is less than the PV.

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

4

±$12,437,500

$10,341,500

N

I/Y

PV

PMT

FV

Solve for

– 4.51%