Problem $4$: Planning for Life

Right after graduating from LSU, you get your dream$-$job with a starting salary $$100,000$ annually

$($paid at the end of each year$),$ which is expected to grow by $5\%$ every year. You plan to stay in

that job for $30$ years and then retire. Your annual contribution to a $401$ K os $15\%$ of your annual

salary $($including your employer's contributions$).$ Your $401$ K is expected to make an annual return

of $11\%$ until you retire. Assume annual payments and annual compounding.

Estimate your final annual salary before retirement.

Estimate how much money you would have in your $401$ K by the time your retire $(t=30).$

At retirement, you decide to draw an annuity for the next $25$ years by placing your funds in

an account that earns a guaranteed $5\%$ per year. Estimate your annual pension.