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I've created my own financial spreadsheet. One of its functions is to allow me to automatically determine how much money I need to save every monthmin order to accumulatexdollars inyamount of time.

Normally, the monthly amountmis calculated by:

1.Dividing the wanted total by the number of monthsn(nis anywhere from 1-12). (In the case where accumulating y would take greater than 12 months then the spreadsheet simply multiplies the annual accumulated amount by 1, 2, 3, etc. years respectively to show what the accumulated amount would be over a greater length of time.) Note that: The amount saved per month is a constant.

2.Calculating what percentagepof my gross monthly incomemis. My wage rate and weekly hours worked are constants; thusp=m/(gross monthly income)*100%.

3.The final value ofmis calculated thusly:

m=p*(gross monthly income) .

(Note: You might ask, 'why go through all that trouble to calculatemif that was already determined in step#1? The answer is simple: In the reality of life, my monthly income fluctuates and is not a perfect constant. One of my main objectives in setting up a budget was to determine a way to divide and distribute income to different items based on their priority. Using a relative system (ie. percentage based) to divide income rater than an absolute system (ie. constant dollar values) made it possible to adapt the budget to the realities of life.)

For each item that I save money for, I have the categories "savings goal" and "current savings".

Now, here is where I start to get confused:

I thought to myself, what if I setup the calculation ofmso that instead of it being a flat rate it were to change depending on the value of the "current savings" for the item in question?

So now,mis calculated like this:

1.m=[tex]\frac{(savings goal)-(current savings)}{n}[/tex]

2.p=m/(gross monthly income)*100% (Note: this step is unchanged.)

3.m=p*(gross monthly income) (Note: this step is also unchanged.)

You will note that the values ofmandpare now in flux and change with each iteration. You will also note that the initial values ofmandpare the same, regardless of whethermandpare constant or variable. Logically, unless the initial rate ofpis higher in the case of variablem's andp's then I don't see how the "savings goal" could be meet in the time allotted, and yet, on the otherhand it seems that it would work in practice. I'm missing/not-understanding something here. Can someone please help me out and explain to me what I'm not quite grasping?

(Note: In my effort to answer this for myself, I tried to derive a formula so that I could graph the variable value ofmand be able to compare it to when it was a constant. Well, that failed tragically as I ended up with a paradox for where the initial value ofmequals itself divided by 100 [ie. m=p*(gross monthly income) ]. Obviously, things like that do not make sense. I'm pretty sure my calculations are accurate so, once again, I believe my underlying problem in one of logic rather than mathematical adeptness. Anyway.......help please? Someone? :3 )

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# Logic Paradox (Need Help)

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