Suppose you have just borrowed $$51,249$ at an annual interest of $5\mathrm{.}7\%$ and must repay the loan in equal installments at the end of each of the next $13$ 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

$$2,764\mathrm{.}88$

$$2,762\mathrm{.}88$

$$2,760\mathrm{.}88$

$$2,766\mathrm{.}88$

$$2,768\mathrm{.}88$