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 $55,000 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 $110,000 saved, and he expects to earn 7% annually on his savings.

Answer 1

Solution

Since he will retire in 10 years therefore according to inflation the value of 55000 in 10 years will be= Amount*(1+inflation rate)^n

=55000*(1+.03)^10

=73915.401

This is the first payment received after retirement

Now the value of this amount will reduce due to inflation , therefore the value (73915.401) must increase every year by 3% , therefore value for year 2 will be 73915.401*1.03, value for year 3 = 73915.401*1.03*1.03 and so on . The calculation has been given in the below table

Now all these values will be discounted @7% to the present values at the time of his retirement

Since the payments occur at the beginning of each year, the present values will be= Amount/(1+r)^n-1

n= year of payment/cashflow

r=.07

Calculation given below

Excel formula

Therefore the total amount needed at the time of retirement= 1214464.699

Now he has already got 110000 saved at the time of retirement

Future value of 110000 = Amount*(1+r)^n

=110000*(1+.07)^10

=216386.65

Therefore the amount needed to be covered =1214464.699-216386.65= 998078.05

FV of annuity =998078.05

FV of annuity= Annuity*((1+r)^n-1)-1)/r

998078.05= Annuity*(1.07^10-1)/.07

Annuity = 72238.39671

Thus his father has to deposit 72238.39671 every year into his account to be able to get retirement income equal to 55000 (In today's value terms) every year after retirement

If you are satisfied with the answer, please give a thumbs up