Question 1149115
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Learn the basic formulas for annuities and loans, and learn how to do the computations using those formulas; or use any of a number of online calculators....<br>
{{{A = (P(1-(1+r)^(-t)))/(r)}}}<br>
A = initial amount
P = periodic payment (withdrawal)
r = annual interest rate
t = number of years<br>
{{{500000 = (40000(1-(1+.078)^(-t)))/(.078)}}}<br>
{{{(500000/40000)*(.078) = 0.975 = 1-(1.078)^(-t)}}}<br>
{{{(1.078)^(-t) = 1-0.975 = 0.025}}}<br>
{{{-t*log((1.078)) = log((0.025))}}}
{{{-t = log((0.025))/log((1.078)) = -49.1}}} to 1 decimal place.<br>
ANSWER: 49.11 years<br>
That answer assumes the first withdrawal is at the END of the first year.<br>
With that interpretation, 50 years after the initial investment there will be an amount still in the investment equivalent to approximately one-tenth of $40,000.<br>