$($Related to Checkpoint $6\mathrm{.}2)($Present value of annuity payments$)$ The state lottery's million$-$dollar payout provides for $$1$ million to be paid in $25$ installments of $$40,000$ per payment. The first $$40,000$ payment is made immediately, and the $24$ remaining $$40,000$ payments occur at the end of each of the next $24$ years. If $12$ percent is the discount rate, what is the present value of this stream of cash flows? If $24$ percent is the discount rate, what is the present value of the cash flows?

a$.$ If $12$ percent is the discount rate, the present value of the annuity due is $ $($Round to the nearest cent.$)$

b$.$ If $24$ percent is the discount rate, the present value of the annuity due is $$.($Round to the nearest cent.$)$