Alex Meir recently won a lottery and has the option of receiving one of the following three prizes: $(1)$ $$64,000$ cash immediately, $(2)$ $$20,000$ cash immediately and a six$-$period annuity of $$8,000$ beginning one year from today, or $(3)$ a six$-$period annuity of $$13,000$ beginning one year from today. $($FV of $$1,$ PV of $$1,$ FVA of $$1,$ PVA of $$1,$ FVAD of $$1$ and PVAD of $$1)($Use appropriate factor$($s$)$ from the tables provided.$)$

$1.$ Assuming an interest rate of $6\%,$ determine the present value for the above options. Which option should Alex choose?