P$5\mathrm{.}4($LO $4)$ Evaluating Payment Alternatives

Howie Long has just learned he has won a $\backslash (\backslash$$ $500,000\backslash )$ prize in the lottery. The lottery has given him two options for receiving the payments. $(1)$ If Howie takes all the money today, the state and federal governments will deduct taxes at a rate of $\backslash (46\backslash \%\backslash )$ immediately. $(2)$ Alternatively, the lottery offers Howie a payout of $20$ equal payments of $\backslash (\backslash$$ $36,000\backslash )$ with the first payment occurring when Howie turns in the winning ticket. Howie will be taxed on each of these payments at a rate of $\backslash (25\backslash \%\backslash ).$

Instructions

Assuming Howie can earn an $\backslash (8\backslash \%\backslash )$ rate of return $($compounded annually$)$ on any money invested during this period, which payout option should he choose?

NOTE: Enter a formula, a cell reference, or a value $($if you are unable to reference a cell$),$ into the yellow shaded input cells.

Lump sum alternative

Annuity alternative

Which payout should Howie select?