My uncle Samuel has $450,000 invested at 6.5%, and he plans to retire. He wants to withdraw $40,000 at the beginning of each year, starting immediately. How many years will it take to exhaust her funds, run the account down to zero?

Answer 1

450000=40000 + 40000(1 - 1.065^-n)/.065

I am using
PV = Paym(1 - (1+i)^-n)/n
but ....
that formula assumes that payments are made at the end of the period, which explains the single 40,000

.66625 = 1 - 1.065^-n
1.065^-n = .33375
log both sides
-n(log 1.065) = log .33375
-n = -17.425

n = appr 17.4 years

(not many years of retirement with money, I have already been retired for 17 years and hope to have lots left. )