Question

1. You have just turned 40 years old and are trying to decide who much money to put into your retirement plan. The plan works as follows: Every dollar in the plan earns 7% per year. You cannot make withdrawals until you retire on your sixty-fifth birthday. After that point, you can make withdrawals as you see fit. You decide that you will plan to live to 95 and work until your turn 65. You estimate that to live comfortably in retirement, you will need $250,000 per year starting at the end of the first year of retirement and ending on your 95th birthday. You already have $200,000 in the retirement plan. You will contribute the same amount to the plan at the end of every year that you work, starting next year. How much do you need to contribute each year to fund your retirement?

Answer 1

First we have find the amount needed to withdraw $250,000 for 30 years (65 to 95) at 7% interest rate. for that use PV function in EXCEL

=PV(rate,nper,pmt,fv,type)

rate=7%

nper=30

pmt=250000

fv=0

type=0

=PV(7%,30,250000,0,0)

PV=$3,102,260.30

In the question, it mentioned that they have already 200,000 in the retirement account. This recevies 7% interest for 25 years (40-65 years)

=200000*((1+7%)^25)=1,085,486.53

So, he has to accumulate 2,016,773.77 (3,102,260.30-1,085,486.53) in 25 years. use PMT function in EXCEL

=PMT(rate,nper,pv,fv,type)

rate=7%

nper=25

pv=0

fv=2016773.77

type=0

=PMT(7%,25,0,2016773.77)

PMT=31,886.24

The annual contributions to fund the retirement account=31,886.24