Question

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 $40,000 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 5% per year
from today forward. He currently has $150,000 saved and expects to
earn a return on his savings of 9% 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 steps.

$

Answer #1

Amount of first payment after retirement = 40,000*(1.05)^10 = $65,155.79

Total amount required on the day of retirement is equal to the present value of future funds required

= 65,155.79 + 65,155.79*PVAF(9%, 24 periods)

= 65,155.79 + 65,155.79*9.7066117

= $697,597.75

Amount at the retirement from current savings = 150,000*(1.09)^10 = $355,104.55

Additional amount required = $342,493.2

Let the amount deposited each year be X

X*[{(1+0.09)^10-1}/0.09] = 342,493.2

15.1929297x = 342,493.2

X = $22,542.93

Hence, amount required to be saved each year = $22,542.93

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 $40,000 has today.
He wants all 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...

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