$1)$ Commentary on the cartoon: The older worker $($Boomer$)$ did not plan well for retirement, and has to work to supplement his retirement check. The Social Security system spends money taken from current workers to pay the benefits of today's retirees. That explains the younger worker's $($Generation X$)$ response to the older worker. Money is taken from his paycheck to fund the older worker's social security check.

In the near future, there will not be enough people working to pay all retirees at today's rate. The Social Security system will go bankrupt. Social Security's options are to increase the money taken from the workers paychecks or decrease the amount of money paid to retirees. Neither option is popular. An alternative is to establish your own retirement fund. We can use the formulas that we worked with in this Module to analyze different retirement plans.

Your Retirement: Plan $1-$ Starting Early

a$)$ Enter your desired amount of money you wish to receive each month while retired $=$ $

$2000$

b$)$ Upon retirement $(40$ years from now$)$ you want to receive $"$x dollars" $($amount of money you choose in Part a$)$ each month for a period of $28$ years. This money resides in an account that pays $5\mathrm{.}3\%$ interest. How much money must be in the account to fulfill your goal?

Amount of money needed $=$ $

$1537885\mathrm{.}80$

$.$

Round your answer to $2$ decimal places as needed.

c$)$ You plan to deposit money every month for $40$ years into an account that pays $5\mathrm{.}8\%.$ What monthly deposit must you make to achieve the amount of money determined in the answer to Part b above?

Payment amount $=$ $

$.$

Round your answer to $2$ decimal places as needed.

d$)$ How much money did you actually deposit into the account?

Total amount deposited $=$ $

$.$

Round your answer to $2$ decimal places as needed.

e$)$ How much money will you actually receive in payments during retirement?

Total amount received $=$ $

$.$

Round your answer to $2$ decimal places as needed.

Your Retirement: Plan $2-$ Waiting Until Middle Age

f$)$ You wait until later to start saving for retirement, and so are depositing money every month for only $20$ years into an the same account that still pays $5\mathrm{.}8\%.$ What monthly deposit must you make to achieve the amount of money determined in the answer to Part b above?

Payment amount $=$ $

$.$

Round your answer to $2$ decimal places as needed.

g$)$ How much money did you actually deposit in this plan?

Total amount deposited $=$ $

$.$

Round your answer to $2$ decimal places as needed.

h$)$ How many times more costly is the monthly payment of Plan $2($saving for $20$ years$)$ compared to Plan $1($saving for $40$ years$)?$

$($Hint: Divide Part f by Part c$).$

How many times more costly $20$ year plan is compared to $40$ year plan $=$

$.$

Round your answer to $2$ decimal places as needed.