Q$3.$

$[30+15=45$ Marks$]$

$($A$)$ Assume that your uncle is now $50$ years old, plans to retire in $10$ years, and 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. 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 and expects to earn a return on his saving $8\%$ 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?