Your mother has just retired. The balance in her investment account is $$200,000$ and she wants to receive monthly payments of $$7138.$ If she receives the payments at the end of the month, and the current interest rate is $8\mathrm{.}1$ percent, compounded quarterly, approximately how many months will her investment account last for? $($Keep three decimal places in your calculations and round the final answer to two decimal places$)$

$($Hint: PV should be inputted as negative number in your calculator$)$Your mother has just retired. The balance in her investment account is $$200,000$ and she wants to receive monthly payments of $$7138.$ If she receives the payments at the end of the month, and the current interest rate is $8\mathrm{.}1$ percent, compounded quarterly, approximately how many months will her investment account last for? $($Keep three decimal places in your calculations and round the final answer to two decimal places$)$

$($Hint: PV should be inputted as negative number in your calculator$)$Your mother has just retired. The balance in her investment account is $$200,000$ and she wants to receive monthly payments of $$7138.$ If she receives the payments at the end of the month, and the current interest rate is $8\mathrm{.}1$ percent, compounded quarterly, approximately how many months will her investment account last for? $($Keep three decimal places in your calculations and round the final answer to two decimal places$)$

$($Hint: PV should be inputted as negative number in your calculator$)$