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.

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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