$1$vy deposits $$1,500$ to Bank $A$ in $6$ months who pays interest at $5\%$ p$.$a$.$ compounded quarterly. Three months later, Ivy transfers the balance to Bank B who pays an interest of $6\%$ p$.$a$.$ compounded quarterly. She makes another deposit of $$2,400$ to Bank B three month after the transfer. Calculate the balance in Bank B $9$ months after the transfer. $($Correct to the nearest cent.$)$