Question

Simon wishes to have $400,000 in a retirement fund 20 years from now. He can create the retirement fund by making a single lump sum deposit today.
How much would Simon need to have on deposit at retirement in order to withdraw $35,000 annually over the 15 years if the retirement funds earns 8
%?

Answer 1

You have conflicting information.

At the beginning of his "retirement period" he will need:
35000( 1 - 1.08^-15)/.08
= 299,581.75

so he would not need $400,000 at that time.

To assure that he will have that $299,581.75 available 20 years from now , he needs a present deposit of
299581.75(1.08)^-20
or
$ 64,274.73

If he wanted $400,000 twenty years from now he would have to make a deposit now of
400,000(1.08)^-20
or $85,819.28

This would supply him with quite a bit more to withdraw annual payments.
Let that payment be P

solve:
400,000 = P( 1 - 1.08^-15)/.08
P = $ 46,731.82