Floyd Ferris invested $$3000$ into an account five years ago and he made payments of $500$ to the account at the end of each quarter. Today his account has grown to have a balance of $$15,927\mathrm{.}50.$ Given that his account offered monthly compounding of interest, the APR on this account is closest to:

Group of answer choices

$5\mathrm{.}40$

$6\mathrm{.}63$

$5\mathrm{.}74$

$5\mathrm{.}25$