$($Compound value solving for $r)$ At what annual rate would the following have to be invested?

a$.$ $$500$ to grow to $$983\mathrm{.}58$ in $10$ years

b$.$ $$300$ to grow to $$450\mathrm{.}22$ in $6$ years

c$.$ $$47$ to grow to $$645\mathrm{.}94$ in $20$ years

d$.$ $$212$ to grow to $$283\mathrm{.}70$ in $5$ years