SOLUTION: You want to be able to withdraw $20,000 each year for 30 years. Your account earns 6% interest. How much do you need in your account at the beginning? $___

Algebra ->  Average -> SOLUTION: You want to be able to withdraw $20,000 each year for 30 years. Your account earns 6% interest. How much do you need in your account at the beginning? $___      Log On


   



Question 1166600: You want to be able to withdraw $20,000 each year for 30 years. Your account earns 6% interest. How much do you need in your account at the beginning?
$___

Answer by ikleyn(52873) About Me  (Show Source):
You can put this solution on YOUR website!
.

Use the general formula  X = W%2Ap%2A%28%281-p%5E%28-n%29%29%2Fr%29.

In this case  the withdrawal annual rate is W = $20000,  the annual compounding rate 
is  r = 0.06,  p = 1 + 0.06 = 1.06, the number of payment periods  is n = 30. So


          X = 20000%2A1.06%2A%28%281-1.06%5E%28-30%29%29%2F0.06%29 = 2912814.42 dollars.     ANSWER


ANSWER.  You need to have  $2912814.42  at the beginning at your account.


Then you get, actually,  30*20000 = 600,000 dollars from your account in 30 years (!)

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.