$3$ We made the following purchases at a store in $2023$:

$500$ on March $1$st;

$200$ on April $10$th;

$250$ on June $19$ th$.$

We then made the following payments to the store: $(1)200$ on March $21$ st$,$ and $(2)200$ on April $15$th$.$ When will a single payment of $550$ discharge the balance? $($Assume June $19$th is the comparison date and a simple rate of interest of $8\%$ applies.$)$

$($a$)11$March

$($b$)19$ March

$($c$)2$ April

$($d$)$ none of the above.