Q$1.$ Assume that your father is now $50$ years old, that he plans to retire in $10$ years, and that he expects to live for $25$ years after he retires $-$ that is$,$ until age $85.$ He wants his first retirement payment to have the same purchasing power at the time he retires as $$40,000$ has today. He wants all. of his subsequent retirement payments to be equal to his first retirement payment. $($Do not let retirement payments grow with inflation: Your father realizes that the real value of his retirement income will decline year by year after he retires$).$ His retirement income will begin the day he retires, $10$ years from today, and he will then receive $24$ additional annual payments.

Inflation is expected to be $5\%$ per year from today forward. He currently has $$100,000$ saved up; and he expects to earn a return on his savings of $8$ percent per year with annual compounding. To the nearest dollar, how much must he save during each of the next $10$ years $($with equal deposits being made at the end of each year, beginning a year from today$)$ to meet his retirement goal? $($Note: neither the amount he saves nor the amount he withdraws upon retirement is a growing annuity.$)$

Q$2.$ A pension plan is offering a lump sum option in lieu of monthly payments to its retirees. Paul Song is eligible for $4,000$ per month over the next $25$ years. If he exercises the lump sum option, the plan will pay him $843,500.$ Song's investment advisor expects a conservatively invested portfolio of assets will earn $0\mathrm{.}5$ percent $(0\mathrm{.}005)$ per month. Based on this information, Song should:

Part A$.$

a$.$ prefer the lump sum option

b$.$ prefer the payment option

c$.$ be indifferent between the two options

Part B:

The present value of a $4,000$ monthly annuity over $25$ years at six percent $($APR with $m=12)$ is: $($show all calculations$)$