A coin sold at auction in $2019$ for $$1,252,000.$ The coin had a face value of $$5$ when it was issued in $1792$ and had been previously sold for $$165,000$ in $1979.$

a$.$

At what annual rate did the coin appreciate from its first 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 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 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$.,32\mathrm{.}16.)$