Please show me how got the answer using an equation and not a financial calculator

(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 11 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 $6,000 payment per year and 22 years duration? % (Round to two decimal places.) Data Table INITIAL AMOUNT OF PAYMENT INTO MONEY DURATION ANNUITY RECEIVED PER OF ANNUITY ANNUITY (AT t = 0) YEAR (YEARS) $50,000 $6.000 22 $70,000 $9.000 16 c $50,000 $6,500 25 (Click on the icon located on the top-right corner of the data table above in order to copy its contents into a spreadsheet.) Done