Question

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 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 $75,000 saved and expects to earn a return on his savings of 8% per year with annual compounding. 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.

Answer 1

Annual income required = Amount today*(1+Inflation rate)^Number of years

= 40,000*(1+5%)^10

= $65,155.79

Total amount required at age 60 = Present value of all withdrawals

= 65,155.79 + 65,155.79*PVAF(8%, 24 periods)

= 65,155.79 + 65,155.79*10.5288

= $751,168.07

Value of savings after 10 years = 75,000*(1.08)^10 = $161,919.37

Additional amount required= $589,248.7

Let annual deposits be x

Future value of annuity = Annual amount* [{(1+r)^n – 1}/r]

589,248.7 = x*[{(1.08)^10 – 1}/0.08]

589,248.7 = 14.486562x

x = $40,675.54

Hence, annual amount required to be saved = $40,676