Ok all you mathmaticians out there,

[Boomyal]

....I need a formula. It has been too many years since my 4 semesters of Algebra.

Here is the deal. There is a sum of money that is to be split by varying percentages, by 5 parties. One of the parties will have their percentage calculated off the total sum and then have certain expenses deducted from it. This of course will leave a bigger balance than would otherwise have occurred.

That remaining balance now needs to be split by the remaining 4 parties, all in proportion to their original percentage interest. In other words, the difference here is the amount of deducted expenses that have thrown back into the remaining pot. You cannot use their original percentages because one party has already been eliminated and the remaining original expenses do not total 100%.

The original percentage interests are as follows. 12.5 (this is the one that will have deductions made), 14.58333%, 14.58333%, 14.58333% and 43.75%.

Objective once again is that the four remaining parties share, proportionate to their original interest, in the expense amount that has been thrown back in the pot.

 

[emoney]

Re: Ok all you mathmaticians out there,

X =( Y - A ) * P (X is their part....Y is the total sum....A is the expenses....P is percentage) for the first party.

B =( C-X) * P (C is Original amount.....X is first party's part from above........P is percentage) per each remaining person.

 

[JB]

Re: Ok all you mathmaticians out there,

I am not a mathematician. I am a speller.

 

[Boomyal]

Re: Ok all you mathmaticians out there,

emoney, I assume that * is for times? Also, I am not necessarily trying to calculate a new percentage for the first party (12.5%) because I will arrive at their total by simple subtraction. Do I need to do that to use the second part of the formula?

 

[Boomyal]

Re: Ok all you mathmaticians out there,

I am not a mathematician. I am a speller.

I guess you just won't get your share then, JB.

Actually I thought 'lover' was the antithesis of 'mathematician'?

 

[Don S]

Re: Ok all you mathmaticians out there,

Here's the short version.

 

[lncoop]

Re: Ok all you mathmaticians out there,

I guess you just won't get your share then, JB.

Way to spell it out for 'im!

 

[Boomyal]

Re: Ok all you mathmaticians out there,

Here's the short version.

I like your sense of brevity, Don!

 

[sccatfish]

Re: Ok all you mathmaticians out there,

I think you need a spreadsheet.

 

[Tim Frank]

Re: Ok all you mathmaticians out there,

....I need a formula. It has been too many years since my 4 semesters of Algebra.

Here is the deal. There is a sum of money that is to be split by varying percentages, by 5 parties. One of the parties will have their percentage calculated off the total sum and then have certain expenses deducted from it. This of course will leave a bigger balance than would otherwise have occurred.

That remaining balance now needs to be split by the remaining 4 parties, all in proportion to their original percentage interest. In other words, the difference here is the amount of deducted expenses that have thrown back into the remaining pot. You cannot use their original percentages because one party has already been eliminated and the remaining original expenses do not total 100%.

The original percentage interests are as follows. 12.5 (this is the one that will have deductions made), 14.58333%, 14.58333%, 14.58333% and 43.75%.

Objective once again is that the four remaining parties share, proportionate to their original interest, in the expense amount that has been thrown back in the pot.

If I understand your criteria:

1) Calculate 12.5 % of the total amount. That is the first amount.
2) Then deduct whatever expenses are due.
3) Take the remainder of the total amount and subtract from it the REMAINING expense total. That will be the amount to be disbursed after expenses.
4) Divide that amount by 87.5....that will equal an "adjusted" 1% of the remaining amount to distribute...or maybe more concisely, 1/87.5th of the total.
5) Multiply the "1% number/fraction" by each remaining % share.(3 x 14.5833 and 1 x 43.75)

That will be correct subject to rounding error... which might total a cent or two.

 

[Boomyal]

Re: Ok all you mathmaticians out there,

Tim, there are no expenses to come out of the balance that will be distributed to the remaining 4 parties so I assume I can skip step 3? It is just that the remaining pot will be enlarged by the expense amount of the 12.5% party, and then only be split by 4.

Another way to look at this is to calculate the payout of the original sum, by the percentages of each party. Then deduct the expenses incurred by the first party (12.5%) and hold it it aside. Now that sum needs to be divied up properly between the remaining 4 parties. I think the same process would be used to either divie up the extracted expense sum OR the remaining balance of the total with the extracted expense sum thrown back into the pot.

I am sure there is a simple, logical way to look at this. That is the reason for this post.

 

[Tim Frank]

Re: Ok all you mathmaticians out there,

Tim, there are no expenses to come out of the balance that will be distributed to the remaining 4 parties so I assume I can skip step 3?

That remaining balance now needs to be split by the remaining 4 parties, all in proportion to their original percentage interest. In other words, the difference here is the amount of deducted expenses that have thrown back into the remaining pot. You cannot use their original percentages because one party has already been eliminated and the remaining original expenses do not total 100%.

I found the quote above a bit confusing...thought you meant there were some other expenses that would just be shared by the last 4 individuals.
Actually if i understand correctly, the expense $$ gets put into the pot for the last 4 shares.

So, step 3 and you should be :
3) add the expense $$ into the remaining "Original Amount".

 

[Boomyal]

Re: Ok all you mathmaticians out there,

Ok, Tim. Here are the results. First the totals were only $10 off.

I started with 25,000 x 12.5% = 3125.
Then subtracted 800 in expenses incurred by the 12.5% party. 3125 (800)= 2325
Subtracting that 2325 from the 25000, that left a balance of 22675 which I divided by the combined percentages of the remaining 4 partners. 87.5 / 22675 = 259.14

I then multiplied the 259.14 by the percentages of each of the remaining 4 partners. The sum of those results, along with adding back the discounted 12.5%'s reduced amount, totaled $25010.24

Pretty nifty, I would say. The key here seemed to be dividing the adjusted balance by the total of the remaining parties percentages.

Thanks

 

[Tim Frank]

Re: Ok all you mathmaticians out there,

Ok, Tim. Here are the results. First the totals were only $10 off.

I started with 25,000 x 12.5% = 3125.
Then subtracted 800 in expenses incurred by the 12.5% party. 3125 (800)= 2325
Subtracting that 2325 from the 25000, that left a balance of 22675 which I divided by the combined percentages of the remaining 4 partners. 87.5 / 22675 = 259.14

I then multiplied the 259.14 by the percentages of each of the remaining 4 partners. The sum of those results, along with adding back the discounted 12.5%'s reduced amount, totaled $25010.24

Pretty nifty, I would say. The key here seemed to be dividing the adjusted balance by the total of the remaining parties percentages.

Thanks

This isn't actually an algebra or arithmetic problem, it is an accounting one.
My Algebra and arithmetic are strong....accounting is not.
What I can say is that $10- is wayyyyy too far off for this....should be at most a penny or two.

I still am not 100% sure what is happening with the money....but here is what I understand now.... (still might be wrong)

The 12.5% recipient has to kick back $800- which is divided pro rata among the remaining 87.5% shareholders.

If so,

I get 14.58333% share at 3779.17 (three times)
The 43.75% share = 11337.50
Add in the 2325 from the 12.5% share and I get 25000.01

 

[Boomyal]

Re: Ok all you mathmaticians out there,

Well Tim, I rechecked all of my calculations and multiplications. Seems I did make an error on multiplying the 14.58333 shares x's the adjusted total (22675), divided by the 87.5%.(259.14)

My revised figures total 24999.74. Now I am only 26 cents off.

The difference seems to be that I came up with 3779.12 for the 14.58333 shares and you came up with 3779.17.

This holds up well when I compare it to the straight distribution without the 800 expense deduction from the 12.5% party.

Those numbers would have been:

43.75 = 10973.50
14.58333 = 3645.53
12.5 =3125.00

 

[Tim Frank]

Re: Ok all you mathmaticians out there,

A simpler approach to dividing the $22675- would be to note that the sum of the 3 smaller shares equals the biggest.
So just divide the $22675 by into two halves = $11737.50 ....give one half to the major "owee" and divide the remaining 1/2 between the final 3....$11737.50/3 = 3779.17 , 3779.17, and 3379.16
You can't divide that 50 cents by 3 evenly...although one option would be to reach into your pocket and add a penny to the short stack.

The complexity in all of this is just making sure that you lay out the credits and debits ....correctly.
e.g. , from the archives => http://forums.iboats.com/showthread.php?t=16852&highlight=missing+dollar


PS ~ your description of multiplying by so many "shares" is a much clearer and better graphically than my description. I'll remember that!