Miss Jones borrowed $$10,000$ at $12\%$ compounded monthly, and agreed to pay back the loan by equal monthly payments over five years. After making the first $10$ payments on time, she missed the next four payments. How much extra interest did Miss Jones have to pay because of the late payments?

a$.$ $$16\mathrm{.}85$

b$.$ $$11\mathrm{.}25$

c$.$ $$179\mathrm{.}15$

d$.$ $$4\mathrm{.}50$

e$.$ $$22\mathrm{.}47$