Question

? that your.father is now 40 years ol? that be plans to retire in 20 years, and that he expects to live for 25 years after he retires, that is, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $75,000 has today (he realizes that the real value of his retirement income will decline year-byyear after be retires). His retirement income will begin the day he retires, 20 years from today, and he will then get 24 additional annual payments. Inflation is expected to be 4 percent' per year from today forward; be currently has $200,000 saved up; and he expects to earn a return on his savings of 7 percent per year, annual compounding. To the nearest dollar, bow much must he save during each of the next 20 years (with deposits being 2. made at the end of each year) to meet his retirement goal? I

Answer 1

Amount required per year = 75,000(1.04)²⁰ = $164,334.24

Amount required on the day of retirement = present value of all withdrawals

= 164,334.24 + 164,334.24*PVAF(7%, 24 periods)

= 164,334.24 + 164,334.24*11.4693

= $2,049,132.94

Value of amount already saved = 200,000(1.07)²⁰ = $773,936.89

Additional Amount required = 1,275,196.05

Let the amount saved each year be x

1,275,196.05 = x*[{(1.07)²⁰ -1}/0.07]

1,276,196.05 = 40.99549x

X = $31,130.16

Hence, amount required to be saved each year = $31,130.16