Problem: Assume you are $32$ years old and plan to retire in $35$ years at age $67.$ You are currently earning $$75,000/$year and expect average annual salary increases of $4\mathrm{.}0\%/$year over the next $35$ years. You have $$0$ saved for retirement. You are trying to determine how much money to save $($invest$)$ each year in your $401($k$)$ Plan to fund your retirement in order to pay yourself $70\%$ of your final salary each year $($that increases with inflation$).[$Remember this is an Annuity Due, so your first annual investment is made in Year $0.$and your final payment is in Year $34.]$ You plan to maintain an investment as a percent of your salary, which simply means your payment into the $401($k$)$ will also increase by $4\mathrm{.}0\%$ per year as your salary increases $4\mathrm{.}0\%$ each year. You believe that you can earn $8\mathrm{.}0\%/$year over the next $35$ years while saving for retirement. Once you retire, you have a life expectancy of $25$ years. You plan to be more conservative in your investments and expect to earn only $5\mathrm{.}0\%/$year on your investments over the $25$ years while in retirement. You also want to maintain your purchasing power by increasing your annual retirement pay by the expected inflation rate of $3\mathrm{.}0\%$ each year. $[$Remember$,$ your first withdrawal will be made in Year $0$ of retirement $($i$.$e$.,$ Year $35$ on the timeline.$]$ Assume that after you withdraw the $25$th payment, you will have $$0$ left in the account. Instructions: $-$ SET CALCULATOR TO BEGIN! $-$ Set up and show your Timeline with payments. You MUST show your work in order to get partial credit. $-$ For this problem it would be better to handwork the problem and save as a pdf before submitting. $-$ BOX in all your ANSWERS! $-$ You may round all answers to the dollar throughout the problem. $-$ Carry your adjusted interest rates out to $6$ decimal places to reduce rounding errors. Questions: $[$NOTE: there are obviously many steps to get to these answersscoring is below.$]1.$ What is your final years salary? What is $70\%$ of your salary? $[$Round to the dollar.$]$

$2.$ How much will you need in your $401($k$)$ at retirement in order to pay yourself $70\%$ of your final years salary, AND have that payment to yourself increase at $3\mathrm{.}0\%$ each year to maintain purchasing power?

$3.$ How much do you need to contribute each year $($i$.$e$.,$ save, invest$)$ over the next $35$ years in order to fund your retirement. Remember, payment into the $401($k$)$ is increasing by $4\mathrm{.}0\%$ each year.