$($Solving for $r$ with annuities$)$ Nicki Johnson, a sophomore mechanical engineering student, receives a call from an insurance agent, who believes that Nicki is an older woman ready to retire from teaching. He talks to her about several annuities that she could buy that would guarantee her an annual fixed income. The annuities are as follows in the popup window:

If Nicki could earn $8$ percent on her money by placing it in a savings account, should she place it instead in any of the annuities? Which ones, if any? Why?

a$.$ What rate of return could Nicki earn on her money if she place it in annuity A with $$6,500$ payment per year and $22$ years duration?

$\%($Round to two decimal places.$)$

Data table

$($Click on the following icon in order to copy its contents into a spreadsheet.$)$

$\backslash$table$[[,$INITIAL,AMOUNT OF$,],[,$PAYMENT INTO,MONEY,DURATION$],[$ANNUITY$,$ANNUITY,RECEIVED PER,OF ANNUITY$],[$A$,$ AT $t=0,$YEAR,$($YEARS$)],[$B$,$$$70,000,$$$6,500,22],[$C$,$$$60,000,$$$6,000,20]]$