whether the examples we've done above are totally accurate or not, the point is you can achieve almost exactly the same result by having a constant % each week... might just need to spend some time on a calculator or spreadsheet first though to work out what that % is for you.
I don't think that's true. By juggling the percentages you can withdraw every week and arrange to withdraw the same amount as if you withdrew only once every 4 weeks (but end up with a lower principal) or end up with the same principal (but withdraw a smaller total).
For example. Suppose you deposit 1000 BTC and decide to withdraw 70% of your interest after letting it compound at 7% per week for 4 weeks.
You'll withdraw 217.55 BTC and leave 1093.23 BTC in the account.
Now we attempt to replicate that by withdrawing a fixed percentage of the interest each week.
If we withdraw 67.81% of the interest each week, we'll end up leaving 1093.23 BTC in the account but only withdrawing 47.46 + 48.53 + 49.63 + 50.74 = 196.38 BTC - we're 21.16 BTC worse off than leaving the interest to compound for 4 weeks.
On the other hand, if we withdraw 75.75% of the interest each week, we end up withdrawing 53.02 + 53.92 + 54.84 + 55.77 = 217.55 BTC, but end up with only 1069.65 BTC left in the account - we're 23.58 BTC worse off than in the first case where we left the interest to compound.
In summary:
weekly withdraw total withdrawn total left in account
--------------- --------------- ---------------------
0% (70% at end) 217.55 1093.23
67.81% 196.38 1093.23
70.00% 202.26 1086.68
75.75% 217.55 1069.65
So we have to chose to either withdraw the same amount (and keep less) or keep the same amount (and withdraw less).
If you think about it, it stands to reason. Withdrawing any amount each week is bound to earn you less than leaving the money to compound for a month before withdrawing. That's why compound interest is 'better' than simple interest.
Edit: added 70.00% weekly withdraw line to table - thanks payb.tc.