SOLUTION: Suppose a man is 25 years old and would like to retire at age 60. ​Furthermore, he would like to have a retirement fund from which he can draw an income of ​$100,000 pe

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Question 1119121: Suppose a man is 25 years old and would like to retire at age 60. ​Furthermore, he would like to have a retirement fund from which he can draw an income of ​$100,000 per year--forever! How can he do​ it? Assume a constant APR of 8​%.
He can have a retirement fund from which he can draw ​$100,000 per year by having ​$_______in his savings account when he retires.

Answer by ikleyn(52754)   (Show Source): You can put this solution on YOUR website!
.
My first idea was to have infinitely many money on the account.


My second idea was to have a printer and print money.


Finally, I got understanding that all he needs is to have so much money in his account that 8% of it is more than 100000, i.e.


0.08*X >= 100000,   i.e.   X >=  = 1,250,000 dollars.


Then each year he will draw 100000, but the bank will return  equal or even greater amount than 0.08*1250000 = 100000, 
so his balance will only increase from year to year.


It is a rough estimation.


If we want to consider more realistic case, when he withdraws 100000 at the first day of the year and the bank compounds 8% at the end of the year, 

then the unknown starting amount X must satisfy inequality

0.08*(X-100000) >= 100000,   which gives


0.08X - 0.08*100000 >= 100000,

0.08X > (1+0.08)*100000


x >=  = 1350000.


Answer.  Having  $1,350,000 or more initially on the account provides the sough condition.


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