Need help writing formula-math done-work shown

Betsy

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May 25, 2020
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This is not homework. I am not a student. Just looking for help writing the formula based on assumptions that I’m not sure I’m looking at correctly.

Please tell me if the math has been done correctly & please show me how to write the formula please.

Please note: I don’t know how to speak math language so I’ve most likely used wrong words or expressions in the calculations. I hope that though not worded properly you’ll be able to follow the numbers & when showing me how to write the formula, please correct the error of my ways. Thank you in advance for any help you can give.

The Problem:
-Grandma died 2 years ago. She left behind her home, a large amount of money in her accounts and 5 siblings, who I’m calling GTCBS, with whom would each receive 1/5 of estate total (et).
-Much of the money left in her accounts was used to pay bills & to make minor & some major home improvements prior to sale of house.
-Once improvements were made and home sale completed, the remaining funds from her accounts were to be added to final sale price of home which would determine remaining estate total (et) to be divided & distributed to GTCBS.
-Prior to sale of home & et determined, sibling B was given a 10,000 emergency advance from his portion of the et.
-Bs understanding was that once home sold, estate tallied & distributions made his allotment would be 10,000(the amount of Bs advance) less than each of the remaining four (GTCS) allotment.
-House sold last week. Sale price & remaining funds totaled 406,150 (et)
-The executor did the following math to calculate allotments for each GTCBS

-What is known:
406,150 is et
-What is assumed:
Bs allotment should be 10,000 (advanced amount) less than the allotment for each GTCS
*************************
This is how the executor did his calculations:

406,150 et
/ 5 GTCBS
=81,230 each allotment

81,230 each
-10,000 Bs advance
=71,230 for Bs allotment

406,150 et
-71,230 Bs allotment
=334,920 remaining et to be distributed among GTCS

334,920 remaining et
/4 GTCS
=83,730 GTCS allotment each

These are the allotments amounts the executor is planning to distribute between the five, GTCBS:
83,730 GTCS allotment each
71,230 Bs allotment from calculation above

**************************
HOWEVER:

83,730 GTCS allotment each
-71,230 Bs allotment from calculation above
=12,500 less for B than GTCS
NOT 10,000 less as B expected for his 10,000 advance

**************************
What follows are additional calculations by B to correct 12,500(executors amount less from Bs allotment than each of GTCS allotment)
so that his allotment is only 10,000 (amount of Bs advance) less than each of GTCS allotment.

**************************
12,500 less for B than GTCS
-10,000 Amount Bs allotment should be less than from that of GTCS
=2500 surplus taken out from B

2500 surplus from B
/5 GTCBS (total original siblings)
=500 excess given to each GTCS
(I’m not really sure how to justify the division by 5 except that it accounts for all 5 siblings. I just know that by the end of these calculations the numbers appear to fall in line)

83,730 GTCS original allotment
-500 GTCS each share of surplus taken from B
=83,720 GTCS each recalculated allotment

83,720 GTCS each recalculated allotment
x4 GTCS
=332,920 total amount GTCS should receive

406,150 et
-332,920 recalculated allotment total for GTCS
=73,230 remaining amount which should be Bs recalculated allotment

83,720 recalculated GTCS allotment
-73,720 recalculated Bs allotment
=10,000 less for B than GTCS AND the amount B was given in advance

**************************
The #s look right to me but once B showed his recalculations to executor (who is just sibling G, not an accountant, no college classes taken, no degree BUT the same goes for B) the executor balked about the 500 asking where B came up with that # even though a handwritten copy of Bs calculations was electronically sent to him so that he could physically see how each step was taken & displayed in detail as, I hope, the calculations above have done for you as well.

The executor has seen the math but he wants the formula written out that proves those calculations to be true & I implore you to please help in that regard as neither B or myself don’t know how to speak ‘math’ much less how to write it out.

I hope my explanations made sense as I’m just deciphering Bs math then trying to make it make sense to you.

I hope you can help & I thank you in advance for any help you are able to provide.
 
I did not read your whole post.

One way of thinking about it.
Imagine that B paid back the $10,000.
Then there would be 416,150 to be shared amongst the 5 siblings. So each will get 83,230. But B did not pay back the money so he gets 73,230 and the rest each gets 83,230. Looks fair to me that B gets $10,000 less than the others.
 
I did not read your whole post.

One way of thinking about it.
Imagine that B paid back the $10,000.
Then there would be 416,150 to be shared amongst the 5 siblings. So each will get 83,230. But B did not pay back the money so he gets 73,230 and the rest each gets 83,230. Looks fair to me that B gets $10,000 less than the others.

I would say that the estate is $416,150 since it includes the $10,000 loan. This is the amount that should be divided by 5. Then B's share is reduced by $10,000.
 
Another way to think about it is to take off $40,000 from the total and give everyone $10,000 except for B. Then split the rest evenly. You will get the same results I got before.
 
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