Assume that your father is now 50 years old, plans to retire in 10 years, and ex
ID: 2812638 • Letter: A
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 $35,000 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 3% per year from today forward. He currently has $25,000 saved and expects to earn a return on his savings of 10% 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.
Explanation / Answer
Solution:
1. Amount need to save in 10 years to match $ 35k purchashing power taking into account 3% inflation would be : 35000*(1.03)^10 = 47037.07
2. Taking into account PV of the above amount, till the age of 60 father would need :
47037.07 / 0.1*(1-(1.10) ^ -25 ) = 426957.4
3. Value of amount saved after 10 years : 25000*1.1^10 = 64843.56
4. Additional saving needs to be done = 426957.4 - 64843.56 = 362113.8
5. Amount to be saved each year for 10 years (taking into account savings rate) : 362113.8 *(-0.1)/(1-1.1^10) = 22720.98