Assume that your father is now 50 years old, plans to retire in 10 years, and...

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Assume that your father is now 50 years old, plans to retire in10 years, and expects to live for 25 years after he retires - thatis, until age 85. He wants his first retirement payment to have thesame purchasing power at the time he retires as $60,000 has today.He wants all of his subsequent retirement payments to be equal tohis first retirement payment. (Do not let the retirement paymentsgrow with inflation: Your father realizes that if inflation occursthe real value of his retirement income will decline year by yearafter he retires). His retirement income will begin the day heretires, 10 years from today, and he will then receive 24additional annual payments. Inflation is expected to be 5% per yearfrom today forward. He currently has $100,000 saved and expects toearn a return on his savings of 4% per year with annualcompounding. To the nearest dollar, how much must he save duringeach of the next 10 years (with equal deposits being made at theend of each year, beginning a year from today) to meet hisretirement goal? (Note: Neither the amount he saves northe amount he withdraws upon retirement is a growing annuity.) Donot round intermediate steps.

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4.4 Ratings (956 Votes)

Value of savings [amount in hand] in 10 Years = 100000*1.04^10 =	$ 1,48,024.43
Value of fixed return income in 10 years = 60000*1.05^10 =	$ 97,733.68
Value of 25 beginning of year retirement income = 97733.681.04(1.04^25-1)/(0.04*1.04^25) =	$ 15,87,875.50
Net amount needed:
Value of retirement payments	$ 15,87,875.50
Value of savings	$ 1,48,024.43
Net amount needed	$ 14,39,851.07
Annual savings needed for next 10 years = 1439851.07*0.04/(1.04^10-1) =	$ 1,19,926.56

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Transcribed Image Text

Assume that your father is now 50 years old, plans to retire in10 years, and expects to live for 25 years after he retires - thatis, until age 85. He wants his first retirement payment to have thesame purchasing power at the time he retires as $60,000 has today.He wants all of his subsequent retirement payments to be equal tohis first retirement payment. (Do not let the retirement paymentsgrow with inflation: Your father realizes that if inflation occursthe real value of his retirement income will decline year by yearafter he retires). His retirement income will begin the day heretires, 10 years from today, and he will then receive 24additional annual payments. Inflation is expected to be 5% per yearfrom today forward. He currently has $100,000 saved and expects toearn a return on his savings of 4% per year with annualcompounding. To the nearest dollar, how much must he save duringeach of the next 10 years (with equal deposits being made at theend of each year, beginning a year from today) to meet hisretirement goal? (Note: Neither the amount he saves northe amount he withdraws upon retirement is a growing annuity.) Donot round intermediate steps.