if i invest 113,000.00 for 20 years what will i have left if i withdraw
7200.00 at the end of each yr?

Hi sara4277:

Thanks for the interesting question. 

Of course, the answer to your question depends on what the interest
rate is on your 20 year investment. I have done some calculations at
different interest rates as an example for you. I have assumed that
you invest the money at the beginning of Year 1 and don't begin to
withdraw until the end of Year 1.

Interest Rate         Balance at End of 20 Years
   3%                        $ 10,623.87
   5%                        $ 61,747.77
   7%                        $142,106.80
  10%                        $347,827.50

In fact, the formula to figure out what you'd have left for *any*
interest rate (say, r) is:

-31000 + 892000*r + 13262000*r^2 + 93936000*r^3 + 435856200*r^4 +
1472880000*r^5 + 3821736000*r^6 + 7852776000*r^7 + 13025298000*r^8 +
17649236800*r^9 + 19668116000*r^10 + 18072496000*r^11 +
13676466000*r^12 + 8480688000*r^13 + 4268251200*r^14 + 1717068000*r^15
+ 539277000*r^16 + 127452000*r^17 + 21326000*r^18 + 2252800*r^19 +
113000*r^20

where r is expressed as a decimal (i.e., 5% = .05)

By manipulating this expression in Maple (a computer algebra software
program), I found that if you can get an interest rate of 2.43% you
will just exactly use up all the money after 20 years. As well, if you
get an interest rate of 6.37% your original investment will remain the
same after 20 years.

I hope this has been of help to you. If you need clarification, please
ask.

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