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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