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Advanced Math/Equity split


QUESTION: We would like to know how to calculate the split of the collateral in our property now it is being sold.

Original house  price  - 565,000
Mortgage 397,000
Initial investment :- 168,00 shares in property split as below.

124,320  ( 74%) - Me
43,680 (26%) Partner


When the property was valued at 835,000 the calculations were as below:-

House price valued at - 835,000
Mortgage value 397,000
New Equity 438,000

324.120  (74%) Me
113,880 (26%) Partner

Then my Partner paid an additional 100,000 off the joint mortgage.. At that time we did not recalculate our new % share in the house. Now we are selling the property, we now need to know how to split the proceeds.

We are selling the house for 1022,500. Since my Partner paid 100,000 as mentioned above, we have both paid off equal sums brining the mortgage value down to 130,000, now leaving 892,500 equity.

Please can you advise the fairest way to  re-calculate our percentages and the sums we should receive on sale . We have been given two options 1) My Partner should have increased his shares by buying my shares giving me the 100,000 or 2) Starting from scratch as if we were buy the house at 835,000 using his 100,000 as part of his deposit, or do you have a different calculation you feel is fairer?

Thank you.

ANSWER: Now since you owned 324,120 and your partner owned 113,880 at the start,
and then your partner paid an additional 100,000, the amount owned for each of you is
324,120 for you 213,880.

To find the percentage for each of you, take your individual amounts over the sum.  That is, the sum is 538,000.  Your share would then be roughly 60% and your partners would be 40%.  If the percentages are carried out, they are really 60.24535316% and 39.75464684%, but it makes it really easy to call the amounts 60% and 40%.

If you start quibbling about a 1/4 of a percent when they are so close to a 10% increment, to much fuss would come up.  As is, they can be taken to be roughly 3/5 (60%) and 2/5 (40%).

So with the 892,000 equity, I would divide it as 530,000 to you and 350,000 for you partner.
That would leave 12,000 left over to have whatever between the two of you.  In the USA, that seems like it would be equivalent to enough to afford a fairly decent vacation together.

---------- FOLLOW-UP ----------

QUESTION: Thank you for your prompt reply.

My next question is - if the % on the original equity of 438,000 was split 74% (me) 26% (partner), surely the new % split you have calculated of 60% (me) 40% (partner) when he added his 100,000, should only be on the difference between the 438 (original equity) and the current equity of 892,000 (454,000). Otherwise surely I would lose out because I would lose 14% of our original equity (438,000)?

Thank You

A mistake was made on one of my numbers in my earlier calculations (swapping a couple of digits in one of the numbers), and not only that, I forgot to account for some of the details of your question.  On that, ignore what I sent so far and let me start again.

The original price was 565,000.  There was 168,000 that was paid on the original,
leaving 397,000 in mortgage.  Of the 168,000 invested, 124,320 was by you and
43,680 was by your partner.

When value of the house was 835,000, and the mortgage value was still 397,000.
The value we owned was then 835,000 - 397,000 = 438,000.

Equal payments were made on the 397,000 to bring it down to 130,000.
That means there was a total payment of 267,000.  This was said to be done equally,
so you each payed 133,500.

This means you payed in 124,320 + 133,500 = 257,820 and
your partner paid in 43,800 + 100,000 + 133,500 = 277,300.
Added together, that gives a total of 525,120 that was paid in.

The house was sold at 1,022,500.  After taking care of the rest of the mortgage,
that leaves 892,500.  According to the total invested by each of you, that makes
your value at 438,193.84 and your partner's value at 454,306.16.

So after studying it in more detail, it looks like the total investment by your partner was a little above yours.  In this way you both receive a roughly 70% payoff on your investment.  Note that I don't take into account the fact that your initial payment was far greater, only in how much your total investments turned out to be.  To look at what you possible might have owned at the start ignores the fact that he put in an extra 100,000 and you both invested another 133,500.

From what I read, that is what it looks like to me.

Please review what I sent any find anywhere that I put down some wrong numbers and point out why.
Thank you and best wishes.

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Scott A Wilson


I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?


Experience in the area; I have tutored people in the above areas of mathematics for over two years in I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.

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