North Georgia Bank offers to lend you $$50,000$ at a nominal rate of $6\mathrm{.}5\%,$ compounded monthly. The loan $($principal plus interest$)$ must be repaid at the end of the year. South Georgia Bank also offers to lend you the $$50,000,$ but it will charge an annual rate of $6\mathrm{.}0\%,$ with no interest due until the end of the year. How much higher or lower is the effective annual rate $($EAR$)$ charged by South Georgia versus the rate charged by North Georgia?

$-0\mathrm{.}65\%$

$-0\mathrm{.}70\%$

$-0\mathrm{.}86\%$

$-0\mathrm{.}78\%$

$-0\mathrm{.}53\%$