Your child's orthodontist offers you two alternative payment plans. The first plan requires a $$4,400$ immediate up$-$front payment. The second plan requires you to make monthly payments of $$144\mathrm{.}09,$ payable at the end of each month for $3$ years. What nominal annual interest rate is built into the monthly payment plan?

a$.19\mathrm{.}09\%$

b$.11\mathrm{.}02\%$

c$.5\mathrm{.}64\%$

d$.11\mathrm{.}69\%$

e$.8\mathrm{.}70\%$