Assume that your father is now $55$ years old, plans to retire in $10$ years, and expects to live for $25$ years

after he retires$$that is$,$ until age $90.$ He wants his first retirement payment to have the same purchasing

power at the time he retires as $$50,000$ has today. He wants all of his subsequent retirement payments

to be equal to his first retirement payment. $($Do not let the retirement payments grow with inflation: Your

father realizes that if inflation occurs 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 $4\%$ per year from today forward. He

currently has $$90,000$ saved and expects to earn a return on his savings of $7\%$ 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.$)$

How points are calculated for this problem:

$$ The value or purchasing power of $$50,000$ when he retires $(2\mathrm{.}5$ points$)$

$$ The value of current amount saved when he retires $(2\mathrm{.}5$ points$)$

$$ Amount of cash needed when retires $10$ years from today to receive annual payment with the

same purchasing power as found in step one $(2\mathrm{.}5$ points$)$

$$ Amount to be saved over the next $10$ years until retirement to be able to withdraw that amount

from step $3(2\mathrm{.}5$ points$)$

$$ BONUS $(7$ POINTS$)$ Find how would the amount to be saved in step $3$ change if the return that

is earned on savings declines from $7\%$ to $5\%$ AND he spends $$10,000$ of the amount currently

saved to buy a car, which leaves $$80,000$ saved.

$($SOLVING IN EXCEL$)$