If Ravi Shekhar bought rare coins for $$40,000$ twelve years ago, and they are worth $$200,000$ now. What annual rate of return did he make on his investment $($assume annual compounding$)?$

$14\mathrm{.}35$ percent

$13\mathrm{.}89$ percent

$13\mathrm{.}52$ percent

$12\mathrm{.}91$ percent

$12\mathrm{.}62$ percent

Please list all formulas, explanations, and steps