Suppose you have just borrowed $$50,951$ at an annual interest of $5\mathrm{.}2\%$ and must repay the loan in equal installments at the end of each of the next $9$ years. By how much would you reduce the amount you owe $($that is$,$ principal$)$ at the end of the first year? $($Hint: Compute annual loan payment first and then the loan amortization schedule for the first year.$)$

Group of answer choices

A$.$ $$4,582\mathrm{.}83$

B$.$ $$4,586\mathrm{.}83$

C$.$ $$4,584\mathrm{.}83$

D$.$ $$4,580\mathrm{.}83$

E$.$ $$4,588\mathrm{.}83$