The $$Brasher doubloon,$$ which was featured in the plot of the Raymond Chandler novel, The High Window, was sold at auction in $2018$ for $$5\mathrm{.}5$ million. The coin had a face value of $$15$ when it was first issued in $1787$ and had been previously sold for $$430,000$ in $1979.$

a$.$ At what annual rate of return did the coin appreciate from its minting to the $1979$ sale? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$

What annual rate of return did the $1979$ buyer earn on his purchase? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$ At what annual rate of return did the coin appreciate from its minting to the $2018$ sale? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$