Lesson Entertainment problem: Uninterrupted withdrawing money from a retirement fund

Entertainment problem: Uninterrupted withdrawing money from a retirement fund

Problem 1

First idea that comes to mind is to have infinitely many money at the account.


The second idea is to have a printer and print money.


Third idea is even better than the two previous. 
Indeed, all this person needs is to have so much money in his account that 8% of it is more than $100,000, i.e.


    0.08*X >= 100000,   which implies   X >=  = 1,250,000 dollars.


Then each year he can withdraw $100,000 (which is 8% of $1,250,000) at the beginning of the year and spend this money for living; 
at the end of the year, at the compounding step, the bank will return  equal or even greater amount than 0.08*1250000 = 100,000 dollars, 
so his balance will be stable or will increase from year to year.


It is a rough estimation.


We can consider more realistic case, when he withdraws $100,000 at the first day of the year and spends it for living; at the end of the year, 

the bank compounds 8% of the remaining amount; it imposes THIS inequality for the unknown starting amount X 

    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 at the account provides the sought condition.