Question

BACKGROUND:

Jason wants to know how much money he needs to have in his retirement account on the day he retires. Jason makes the following ASSUMPTIONS:

--He will withdraw a DIFFERENT amount from his retirement account each year he is retired. He will adjust the withdrawals for inflation each year, following his first annual withdrawal.

--Jason wants to withdraw the equivalent of $75,000 (in terms of today's dollars) in the FIRST year he is retired. Following this, each withdrawal will be 3% larger than the last (withdrawals will be increased each year by 3% to compensate for expected inflation rate of 3% DURING retirement).

--Inflation is expected to be 2.5% per year between now and when Jason retires.

--Jason will retire in 30 years.

--Jason will be retired for 25 years.

--Jason expects his money to earn 6% annualy DURING his retirement.

--Jason expects his retirement account value to drop to zero ($0.00) at the end of his retirement.

Answer 1

Let us assume that Jason withdraws the first amount on the day of retirement and does so for 25 years

The amount required by Jason on the 1st withdrawal (30 years from today) = 75000*1.025^30 = $157317.57

All the subsequent withdrawals will be 3% higher each year

So, amount of money required on the day of retirement = present value of withdrawals

= 157317.57 + 157317.57*1.03/1.06+ ... +157317.57*1.03^24/1.06^24

= 157317.57*(1-(1.03/1.06)^25)/(1-1.03/1.06)

=2846828.01

= $2,846,827.98

NOTE : If Jason starts withdrawing the amount after 1 year from retirement

Amount required = 157317.57*1.03/1.06+ ... +157317.57*1.03^24/1.06^24+157317.57*1.03^25/1.06^25

=157317.57*1.03/1.06*(1-(1.03/1.06)^25)/(1-1.03/1.06)

=$2,766,257.38