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$)$ Retirement 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 detailed work in order to get full credit.$-$ For this assignment, it would be better to type or handwork the problem and save as a pdf before submitting.$-$ BOX in all your ANSWERS!$-$ Round all final answers to the nearest cent throughout the problem. Use a maximum number of decimals for intermediate answers that serve as inputs to subsequent steps in the problem, in order to reduce rounding errors.$-$ 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. Scoring: $1.$ Readability of your Exam. Is it organized, do you show all work, are your answers BOXED in$,$ etc. $(10$ points$)2.$ Correctly work problem as an Annuity Due $(10$ points$)3.$ Calculate the FV of salary and $70\%$ of salary as first withdrawal from your $401($k$)$ in retirement. $(15$ points$)4.$ Do you show a Timeline and is it labeled properly? $(15$ points$)5.$ Calculate adjusted interest rate for Retirement Annuity section. $(10$ points$)6.$ Calculate the PV for the Retirement Annuity. $(10$ points$)7.$ Calculate the adjusted interest rate for the saving$/$investing sections of the problem. $(10$ points$)8.$ Calculate the adjusted FV correctly that is used to determine amount to save each year. $(10$ points$)9.$ Calculate the amount you need to save each year; where payment increases as salary increases. $(10$ points$)$