You currently have a retirement portfolio balance of $$800,000.$ You recently met with your financial advisor and determined you need to have $$2\mathrm{.}032$ million saved before you can retire.

$($a$)$ If you are able to earn a return of $5\%/$year and don$$t plan any further contributions, how much longer do you have to work before you can retire?

$($b$)$ If you instead could earn $8\%/$year$,$ how much long would you have to work?

$($c$)$ What annual rate of return would you need to earn in order to retire in $12$ years?