Assume you are $30$ years old and plan to retire in $37$ 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 $37$ 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 $36.]$ 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 $37$ 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 $3\mathrm{.}1\%$ each year.

$[$Remember$,$ your first withdrawal will be made in Year $0$ of retirement $($i$.$e$.,$ Year $37$ on the timeline.$]$ Assume that after

you withdraw the $25$th payment, you will have $$0$ left in the account.

$2.$ Calculate the FV of salary and $70\%$ of salary as first withdrawal from your $401($k$)$ in retirement.

$3.$ Calculate adjusted interest rate for Retirement Annuity section. Use $6$ decimal places.

$4.$ Calculate the PVA for the Retirement Annuity.

$5.$ Correctly work problem as an Annuity Due

$6.$ Calculate the adjusted FVA correctly that is used to determine amount to save each year.

$7.$ Calculate the adjusted interest rate for the saving$/$investing section of problem. Use $6$ decimal places.

$8.$ Calculate the amount you need to save each year; where payment increases as salary increases.

$9.$ Correctly work problem as an Annuity Due