A coin sold at auction in $2019$ for $$2,897,000.$ The coin had a face value of $$10$ when it was issued in $1795$ and had previously been sold for $$310,000$ in $1970.$

a$.$

At what annual rate did the coin appreciate from its first minting to the $1970$ 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 $1970$ 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 $2017$ sale? $($Do not round intermediate calculations and

rate of return from $1795$ to $1970$ is $6\mathrm{.}08$

rate of return from $1970$ to $2019?$

rate of return from $1795$ to $2019$ is $5\mathrm{.}83$