I am reading Henk Tijms' "Understanding probability" and have become a bit confused.(adsbygoogle = window.adsbygoogle || []).push({});

A man deposits $100,000 in a pension fund for 20 years with an average growth of 14%. Assuming a fixed rate of growth of 14%, the book tells me that the equation below, solved for x, will give me the amount each year so that the initial investment capital, which must remain in the fund for 20 years, remains undisturbed

(1+r)[itex]^{20}A - [/itex][itex]\sum[/itex][itex]^{19}_{k=0}[/itex](1+r)[itex]^{k}[/itex]x =0

This gives $15098.

Doesn't this amount breach the condition of keeping the $100,000 undisturbed after the first year? Aren't we down to $98902 after the first withrawl of $15098?

Secondly, could someone please explain to me how the equation works? It seems to be the undisturbed total in the fund after 20 years of investment at 14% minus the sum of all the growth multiples for 1 years investment, 2 years investment .... 20 years investment multilplied by x (the amount he can "safely" withdraw). I can't really get my head round it.

In case I have misinterpreted the book here is the page I am referring to:

http://books.google.co.uk/books?id=...ntleman would like to place $100,000"&f=false

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# Statistics: Pitfalls of averages

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