Holly Daze has taken out a ten$-$month zero$-$coupon loan of $$3,000.$ If the lender charges $7\mathrm{.}2\%$ per year compounded quarterly, what is the amount she must pay back at the end of the loan?

A$)$ $$3,183\mathrm{.}81$

B$)$ $$3,174\mathrm{.}19$

C$)$ $$3,044\mathrm{.}93$

D$)$ $$3,169\mathrm{.}47$

E$)$ $$3,180\mathrm{.}00$

The correct answer is a$).$ Please do not use excel and explain your steps.