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.

$1.$ Estimate your final annual salary before retirement.

$2.$ Estimate how much money you would have in your $401$K by the time your retire $($t $=30).$

$3.$ 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.