Thread: In suggestions, but may be missed.

Posted: Thu Jul 28, 2005 8:40 pm Post subject: Simple mathematics suggestion.
I am a bit long in the tooth for solving simple equations as it was 50+ years ago since I was at university.
It would be very interseting if someone were to produce an equation for the most effective removal of money from the loan programme. It could be in the form of a family of graphs or simply a more complex equation where the variable is the time in months for the total length of ROL removal to withdraw, where you decide the number of months.

eg:- 40% withdraw ongoing roughly equates to a constant.
50% gives a slight increase.
60% gives a noticeable increase.
and so on------

50% would eventually overtake 40% but be less at first.
60% would eventually overtake 50% and so on------

A mathematical formula is therefore required if we have
an able mathematician amongst us. Please advise.

Huhubug,

did you try the available simulators yet (search the forum on 'simulator' and you'll get several hits)? You can use them to compare different strategies quite easily.

Most of them are Excel worksheets. In some of them (or when you contact their creators), you might be able to get the formulas behind. But probably you won't need these formulas anymore as the time series they produce when you'll have entered your different parameters are, I guess, exactly what you need. You can enter a variable withdrawal % at every day you like,... And at least in some of them, you'll be able to 'grab' and copy the resulting series of numbers to your own worksheet to produce the graphs you're looking for.

If these can't help you, I can post lateron something of a formula you can start with (and other might start debating on... as I probably will overlook plenty of things).

In case the simulators didn't help you out...
There were elaborate posts on the old forum which would have probably given you formulas, better examples of results & strategies. But I don't have them stored. Below you find at least a very basic start. I guess it will probably be broken down by the real math guys & girls over here... as I might have forgotten plenty of things... but that's OK :-).
So... fwiw... (I probably won't spend more time to correct it... but it has been a nice exercise) Here's my shot...

1. The basic formula will be something like this:
FUND0 = PRINCIPAL * 1.02EXP(D)
with FUND0 = the amount available in p*p* generating 2% after D trading days
with principal = the amount of money you have loaned to start with
with D = the number of trading days since you started (1)
with 1.02 = growth rate at 100% reloan (of the 2% intrest you get)

E.g. After three trading days 1000$ principal adds up to 1000$ * 1.02³ = 1092,73.

2. Consider one period of PP% withdrawal from day W up to day D. During that period, you'll decrease that 1.02 growth rate,
e.g. 00% reloan/100% withdrawal equals 1.00 growth rate
e.g. 50% reloan/50% withdrawal equals 1.01 growth rate
e.G. 20% reloan/80% withdrawal equals 1.004 growth rate
Or:
FUND1 = PRINCIPAL * 1.02EXP(W) * 1.XXXEXP(D-W)
WITHDRAWAL1 = PRINCIPAL * 1.02EXP(W) * PP% * (D-W)
with 1.XXX = growth rate
with PP% = % withdrawal = 1 - % reloan
with D-W = withdrawal period in trading days

3. Basically, for each period with a changed withdrawal % in your time line, you add another factor to the formula with the appropriate three parameters indicating start day, end day and resulting growth rate.
E.g. to add a period up till some day F in the future, you just expand the formula to:
FUND2 = FUND1 * 1.YYYEXP(F-D)
WITHDRAWAL2 = WITHDRAWAL1 + (FUND1 * pp% * (F-D)
with FUND1 = fund at the end of trading day D
with 1.YYY = growth rate (from trading day D to F)
with pp% = % withdrawal = 1 - % reloan (idem)
with D-F = newly added withdrawal period in trading days

If for this period, you reloan 100%, growth rate will be 1.02 again.
Etc etc etc

4. Some important factors aren't included in this formula yet but lower the growth rate (and as such the compounding):

- there is no continuous growth. You may only reloan in quanta (units) of 25$. This slows down the compounding... but...
The relative effect of this is smaller when funds are big. E.g. at 100% reloan
i) 425$ produces 2% = 8,5$ a day. This amount is too small to be reloaned immediately... it's compounding value is 0% (and not 100% as in the formula above). You'll have to wait until the third day to have 3*8,5=25,5$, enough to buy yourself your first unit of 25$ to add to your funds and start compounding.
ii') 10,000$ produces 2% = 200$. This amount can immediately be reloaned completely... so it's compounding value is 100% that particular day. It will still vary but never fall that deep again. Imagine for example
ii bis) 9,999$ produces 2% = 199,98$ of which 175$ can immediately be reloaned... So the intrest will still be compounding at 175/199,98 = 87,5% that day... being the lowest compounding ratio you'll ever get from this point (as long as your funds keep growing).
And the relative effect of this is also smaller when reloan % is high (idem).

- there is only growth for a limited period of time. Your principal and reloaned units have a lifespan of only 180 'living' days in which they moreover will only provide 2% growth during a limited number of (120-150?) trading days.

5. Monthly added 'free' roi, fees, charity reductions etc not included.