The "Brasher doubloon," which was featured in the plot of the Raymond Chandler novel, The High Window, was sold at auction in 2014 for $4,582,500. The coin had a face value of $15 when it was first issued in 1787 and had been previously sold for $430,000 in 1979. At what annual rate did the coin appreciate from its minting to the 1979 sale? What annual rate did the 1979 buyer eanon his purchase? at what annual rate did the coin appreciate from its minting tothe 2014 sale?

The time line from minting to the first sale is:

0-192

$15 - $430,000

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:

r = (FV/PV) 1/t - 1

r = ($430,000/$15) 1/192 - 1

r =.0549, or 5.49%

The time line from the first sale to the second sale is:

0-35

$430,000 - $4,582,500

we can use either the FV or the PV formula. Using the FV formula, that is:

FV = PV (1 + r) t

Solving for r:

r = (FV/PV) 1/t - 1

r = ($4,582,500/$430,000) 1/35 - 1

r =.0699, or 6.99%

The time line from minting to the second sale is:

0-227

$15 - $4,582,500

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 = ($4,582,500/$15) 1/227 - 1

r =.0572, or 5.72%