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 $60,000 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 3%. He currently has $90,000 saved, and he expects to earn 10% 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

SOLUTION

Since at the time of retirement,he wants income ,which has same purchasing power as today

Today income = 60000

Threfore amount which will have same purchasing power as today= Today income*(1+inflation rate)^Number of years to retirement

=60000*(1+.03)^10

=80634.9828

Now He will get a sum=80634.9828 every year beginning for 25 years

PV of 80634.9828 every year beginning for 25 years= Annuity amount*(((1-(1/(1+r)^n))/r))*(1+r)

where n= number of years = 25

r= rate of intrest= 10%

Annuity amount=80634.9828

PV of 80634.9828 every year beginning for 25 years=80634.9828*(((1-(1/(1+.1)^25))/.1))*(1+.1)

=805119.662

Now This is the value he must have in his account at the time of retiremen=805119.662

Future value of 90000 which he has in his account now at the time of retirement= 90000*(1+intrest rate)^number of years

=90000*(1.1)^10=233436.8214

Therefore he needs (805119.662-233436.8214=571682.8406)571682.8406 more value after 10 years

571682.8406 is the future value of annuity he must deposit every year for next 10 years

Future value of annuity= Annuity amount*((1+r)^n-1)/r)

571682.8406=Annuity amount*((1+.1)^10)/.1)

Annuity amount=35870.47

He must deposit 35870.47 every year for next 10 years

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