eBook

Required Annuity Payments

Assume that your father 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 $$55,000$ has today. He wants all of his subsequent retirement payments to be equal to his first retirement payment. $($Do not let the retirement payments grow with inflation: Your father realizes that if inflation occurs the real value of his retirement income will decline year by year after he retires$).$ His retirement income will begin the day he retires, $10$ years from today, and he will then receive $24$ additional annual payments. Inflation is expected to be $6\%$ per year from today forward. He currently has $$75,000$ 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.$)$ Do not round intermediate calculations. Round your answer to the nearest dollar.

$