If upon retirement in 20 years Simon plans to invest $400,000 in a fund that earns 5%, what is the maximum annual withdrawal he can make over the following 15 years
As you can see from the related questions below, this identical question has been asked for the third time without any reply.
Probably because the wording is strange and not very clear.
1. Does he have $400,000 now and invests it for 20 years, and then begins his withdrawals
or
2. Are the $400,000 available to him 20 years from now?
if it is the last case, why even mention that he wants to retire 20 years from now, it would not enter the picture.
A further problem is that you don't say when the first widrawal is made.
Is it made at the beginning of the 20th year or at the end of the 20th year.
The standard formulas apply to a general annuity, that is, payments are considered to be made/received at the end of a period.
Interpretation #2, first payment at end of year 20
400,000 = paym( 1 - 1.05^-15)/.05
paym = $38,536.92
for interpretation #1,
400,000(1.05)^20 = paym( 1 - 1.05^-15)/.05
this time the payment = $102,249.91
wow, what a difference!