sixtyforty wrote: ↑Sat Mar 23, 2019 8:18 am
**Account (B) **The owner has to continually sell shares to get an equivalent 6% cash, which not only leads to lower returns (fewer shares), but

**at some point in the future the shares will go to ZERO.**

This is the error. If you are selling 3% of shares per year, that means each year you are keeping 97% of shares. So, after several years, you have:

.97 * .97 * ... * .97 * .97 shares. So long as the number of years is finite, then you will have a non-zero number of shares. Meanwhile, each of those shares keeps increasing in value, exactly counteracting the reduction in shares.

If you are worried about an infinite number of years, then we should change the question to what is the value after an infinite period of time:

Value = shares * price

Assume first year, you had 1 share with price of $1

shares = 0.97 * ... * 0.97

price = 1.03 * ... * 1.03

Value = 0.97 * ... * 0.97 * 1.03 * ... * 1.03

Value = (0.97 * 1.03) * ... * (0.97 * 1.03)

Value = 1 * ... * 1

Value = $1

So, even taking the limit as time goes to infinity, you would still have the same amount of money. Note, that I cheated a bit in stating that 1.03 * 0.97 is equal to 1. It isn't of course, but under your plan, if you had growth of 3%, you should really only sell 2.912...% rather than 3% in order to collect 3% of your original investment (as each share is worth 3% more, the value of the sale is worth 3% of the original investment even though you sell slightly fewer than 3% of shares). If you were to plug in the exact number of shares you are supposed to sell rather than 3%, then 1.03 * [1 - percent you sell] would equal exactly 1.

So, forever and ever, your investment will be remain worth the same amount (with your given assumptions). Now, you might argue that mutual fund shares and ETFs can't be split into infinitely small units. However, if the NAV/share price was to get high enough, then a split would almost certainly occur. So, in practice, the quantization doesn't really change anything.