SOLUTION: Sophie is 30 years old. However, she is already planning for retirement. She plans on retiring in 35 years when she will be 65 years old. Sophie believes she will live until she is

Question 1135293: Sophie is 30 years old. However, she is already planning for retirement. She plans on retiring in 35 years when she will be 65 years old. Sophie believes she will live until she is 95.
In order to live comfortably, she thinks she will need to withdraw $15,000 every month during retirement. These monthly withdrawals will be made at the beginning of each month during retirement
During retirement, Sophie expects to earn 5% per year compounded semi-annually.
a) How much money does she need when she retires at the age of 65?
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.

Let me re-formulate the problem, for clarity, in this way.

    How much money should Sophie have ah her account at the beginning to withdraw  $15000 every month (at the beginning of each month)

    during 30 years, if her account earns 5% per year and is compounded semi-annually ?

Solution

It is the same and it works in the same way as if Sophia withdraws $15000*6 = $90000 at the beginning of every semi-annual period,
and the account is compounded semi-annually at 5% per year.


Use the general formula  X = .

In this case  the withdrawal semi-annual rate is W = $15000*6 = $90000,  the semi-annual compounding rate 
is  r = 0.05/2 = 0.025,  p = 1 + 0.025 = 1.025, the number of payment periods  is n = 30*2 = 60. So


          X =  = 2,851,324 dollars.     ANSWER


ANSWER.  To provide her goal, Sophie needs to have  $2,851,324  at the beginning at her account.

Solved.

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See my lessons in this site associated with annuity saving plans and retirement plans

    - Ordinary Annuity saving plans and geometric progressions
    - Annuity Due saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans
    - Withdrawing a certain amount of money periodically from a compounded saving account (*)
    - Miscellaneous problems on retirement plans

and especially lesson marked (*) in the list as the most relevant to the given problem.

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