Question

Rob and Laura wish to retire in 25 years. They want to be able to withdraw $40,000 per year in today’s dollars during retirement. They expect to earn 8% during their saving years and a 2% real return during their retirement. They expect to live 30 years after retirement, hence making 30 annual withdrawals. Inflation will average 3% per year.

a) What is the value of their first withdrawal in 26 years?

b) How much do they have to have saved in 25 years to fund their retirement?

c) What equal annual payment must they make during their saving years (25) to meet this goal?

d) If they could put away one lump sum today to fund the retirement, how much would it be?

Answer 1

Part (a):

Given,

Value of retirement withdrawal in today’s dollar (A)= $40,000

Inflation rate (i) = 3%

Time till first withdrawal (n) = 26 years

Value of first withdrawal in 26 years= A*(1+i)^n

=40,000*(1+3%)^26 = $86,263.65

Part (b):

Rate of real return during retirement = 2%

Nominal rate= Real rate + Inflation= Real rate*(1+i)+I

= 2%*1.03+0.03= 5.06%

Amount required to be accumulated in 25 years= Present Value of retirement payments (growing annuity)= $1,875,728.16 as follows:

Part (c ):

Equal annual payment to be made during the 25 years of saving period (interest rate at 8%) =$25,657.67 as follows:

Part (d): Lump sum amount needed to fund retirement= F/(1+r)^n

Where

F= Future value required ($1,875,728.16)

r= interest rate= 8%

n= period= 25 years

Lump sum amount needed today= 1,875,728.16/(1+8%)^25 = $273,889.90