SOLUTION: We received a lump sum payment of $500,000 that we invested at 7.8% interest, compounded annually. We plan on withdrawing $40,000 every year. How long will the money last?

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Question 1149115: We received a lump sum payment of $500,000 that we invested at 7.8% interest, compounded annually. We plan on withdrawing $40,000 every year. How long will the money last?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


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....

A+=+%28P%281-%281%2Br%29%5E%28-t%29%29%29%2F%28r%29

A = initial amount
P = periodic payment (withdrawal)
r = annual interest rate
t = number of years

500000+=+%2840000%281-%281%2B.078%29%5E%28-t%29%29%29%2F%28.078%29

%28500000%2F40000%29%2A%28.078%29+=+0.975+=+1-%281.078%29%5E%28-t%29

%281.078%29%5E%28-t%29+=+1-0.975+=+0.025

-t%2Alog%28%281.078%29%29+=+log%28%280.025%29%29
-t+=+log%28%280.025%29%29%2Flog%28%281.078%29%29+=+-49.1 to 1 decimal place.

ANSWER: 49.11 years

That answer assumes the first withdrawal is at the END of the first year.

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.