Question

A coin sold at auction in 2017 for $1,965,500. The coin had a face value of $5 when it was issued in 1794 and had previously been sold for $305,000 in 1971. a. At what annual rate did the coin appreciate from its first minting to the 1971 sale

Answer 1

Answer:

0.0642 or 6.42%

Explanation:

The period 't' between the year when the coin was issued, 1794, and 1971 is:

$t=1971-1794 \\t=177\ years$

If the coin had a value of $5 and after a period of t=177 years it was worth $305,000, the annual tax rate by which the coin appreciated is determined by:

$305,000 = 5*(1+r)^{177}\\r=\sqrt[177]{61,000}-1\\r=0.0642=6.42\%$

The annual rate was 0.0642 or 6.42%.