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I'm mathematically impaired/ignorant and trying to figure out the difference in earnings between my partner and I to work out a fair split of the bills.

So; I earn £2060 per month and partner earns £1650. As a percentage, how much more than her do I earn?

Therefore; If we had a mortgage payment of £850, by what percentage should we split the figure by so it’s proportionate to the difference in our earnings.

Any help sincerely appreciated,

M.

Matt
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2 Answers2

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Your combined earnings are $2060+1650$. So if you will split the rent in proportion to your earnings, you should pay $$850\times \frac{2060}{2060+1650}$$ and your partner should pay $$850\times \frac{1650}{2060+1650}.$$ The amounts are (to $2$ decimal places) $471.97$ and $378.03$ respectively.

As to your question about percentage, you earn $$\frac{2060-1650}{1650}\times 100\%,$$ that is, about $24.85\%$ more than your partner. I believe that this gives a less clear path to seeing what your rent contributions should be.

Remark: There is a good argument that the contributions should be proportional to after tax income rather than income. That argument may not please your partner.

André Nicolas
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  • Thanks to both of you for the help.

    Out of curiosity - Why do you think this gives a less clear path?

    She wants everything to be '50/50' with money but I argue that's not fair on her as I earn more. I'm trying to find a way so that it's proportionately equal.

    Interested in any thoughts people have.

     – Matt Oct 05 '13 at 01:03
  • In my experience, people have trouble with the concepts $x%$ more than, $y%$ less than. You should pay $24.85%$ more than your partner. So the rent should be split in the ratio $124.85:100$. To find your contribution, it turns out that we should multiply $850$ by $\frac{124.85}{224.85}$. But my feeling is that this is less obvious than the argument I gave in the answer. – André Nicolas Oct 05 '13 at 01:17
  • Is that latter example more so in the name of tidy maths and the former for ease of practical application? – Matt Oct 05 '13 at 01:25
  • I think a mathematician would be unlikely to use the percentage version of the argument. And I believe that for practical applications also, the approach in the answer (no percentages) is more understandable. – André Nicolas Oct 05 '13 at 01:28
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You earn more than her : (2060-1650)/1650 * 100% = 24.85 % ,

You should pay for the mortgage : 850*2060/(2060+1650)=850*2060/3710 = 471.96 ,

Your gf should pay the rest

Peter
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