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 BEGINSet up and show your Timeline with payments. You MUST show your work in order to get partial credit.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.