Question

Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $50,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 4%. He currently has $115,000 saved, and he expects to earn 9% annually on his savings. How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Do not round your intermediate calculations. Round your answer to the nearest cent.

Answer 1

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

= 50,000*(1+4%)^10

= $74,012.21

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

= 74,012.21 + 74012.21*PVAF(9%, 24 periods)

= 74012.21 + 74,012.21*9.7066

= $792,419.13

Value of savings after 10 years = 115000*(1.09)^10 = $272,246.82

Additional amount required= $520,172.31

Let annual deposits be x

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

520,172.31 = x*[{(1.09)^10 – 1}/0.09]

520,172.31 = 15.1929297x

x = $34,237.79

Hence, annual amount required to be saved = $34,237.79