You are given the following information:

Date of first payment: $4/1\frac{?}{2021}$

Frequency of payments: Every $3$ months

Number of payments: $40$

Quarterly decrease in payment: $300$

Interest rate: $8\%$ nominal, compounded quarterly

Present value of remaining payments as of $1/1/26$ right after the payment for $1/1\frac{?}{26}$: $50,000$

How much is the first quarterly payment $($round to the nearest hundred$)?$

$($A$)5,700$

$($B$)5,800$

$($C$)11,700$

$($D$)11,800$

$($E$)11,900$