Expert: Steve Holleran - 3/16/2007

Question
$100,000 invested earning 5% interest per year. withdrawling $9456 from this $100,000 per year for ten year.  What is bal of investment at end of ten years... (I am comparing to an anunity.) thanks  Bill

Answer
Hi Bill,

Actually, from the info you've given, I think the fastest and easiest way to do this is just to use a calculator ( I am using a TI-83+) and make use of the simple operation keys.

You basically want to take $100,000, multiply it by 1.05 (that takes 5% and adds it to what you started with), then subtract the $9456.  You should be showing $95,544.
Then just take that answer, multiply it by 1.05 again, and subtract the 9456, getting $90,865.

(If you have a graphing calculator, once you get the 95544 on the screen, just enter "*1.05 - 9456" and the "enter" key repeatedly, and you'll get the results one right after the other).

The amount I came up with after 10 years is $43,952.

There is a formula you can use, but its pretty cumbersome and involves sigma notation:

If we let t stand for the # of years, and B the balance after t years and "SUM" stand for a sigma sign, it would be :

B(t) = 100000(1.05^t) - 9456 * SUM[1.05^k]
                              As k =0 to (t-1)

So for 10 years it would look something like:

B(10) = 100000(1.05^10) -9456*[1.05^6 + 1.05^5 + 1.05^4
                               + ... + 1.05^1 + 1]

I think its faster just to calculate it directly.

Hope this is what you were looking for.

Steve Holleran