Suppose you borrowed $$13,000$ at a rate of $8\mathrm{.}2\%$ and must repay it in $4$ equal installments at the end of each of the next $4$ years. How large would your payments be$?$

a$.$ $$4,316\mathrm{.}00$

b$.$ $$2,876\mathrm{.}46$

c$.$ $$3,643\mathrm{.}68$

d$.$ $$4,454\mathrm{.}43$

e$.$ $$3,942\mathrm{.}46$