Abel and Cynthia are looking forward to retirement and hope to be able to retire when they are $67.$ They would like to maintain their current standard of living during retirement and plan to remain in their current house $($whichever your group decided$)$ during retirement. In order to maintain their standard of living, they estimate that they will need $$100,000$ annually in today$$s dollars. They can also expect to receive an annual benefit from social security of $$55,000$ in today$$s dollars. Given Abel and Cynthia$$s health and family history, a conservative estimate for his life expectancy is $95$ years for both of them. $($Students are encouraged to address this problem with their TI BA Plus Financial Calculators.$)$

a$.$ What lump sum amount will Abel and Cynthia need at retirement in order to maintain their standard of living until age $95?$ Assume that the Cantu are investigating an annuity contract with an insurance company that will promise a $3\%$ rate of return on their investments $($their post$-$retirement return$).$ Assume that inflation averages $2\mathrm{.}25\%.$ Round all amounts to the nearest dollar $***$Abel & Cynthia's current age Both are born in $1991***$