A coin sold at auction in $2019$ for $$3,158,000.$ The coin had a face value of $$2$ when it was issued in $1786$ and had been previously sold for $$420,000$ in $1971.$

a$.$ At what annual rate did the coin appreciate from its first minting to the $1971$ 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 did the $1971$ 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 did the coin appreciate from its first minting to the $2019$ sale? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

$\backslash$table$[[$a$.$ Rate of return from $1786$ to $1971,\%$