Vanessa's lawyer gave her the following two options to settle her invoice:

$($a$)$ $$1,800\mathrm{.}00$ in $1$ month and the balance of $$2,300\mathrm{.}00$ in $4$ months.

$($b$)$ Two equal payments, one in $31$ days and the other in $9$ months.

If money earned $3\mathrm{.}20\%$ p$.$a$.,$ what was the value of the equal payments in Option $($b$)$ such that it is equivalent to the payments in Option $($a$)?$ Use now as the focal date for this question.