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Say I have listed my house for sale for $100,000 and I would like to net 90% of my asking price. I have to pay a 2% commission to the buying agent and that commission will be taxed at 13%. How do I calculate this? Also how does the calculation change if the full sale price is taxed and not just the 2% commission.

If s is my selling price, a is my original asking price, p is my desired net percentage, c is my commission rate, and t is the tax rate on my commission then I think it should be something like:

s=pa+(cts)

But I don't see how I can reduce this to a reusable equation where I can just plug in the variables and get s.

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1 Answer 1

up vote 3 down vote accepted

Let $s$ the selling price. Then the commission is $cs$. I will assume that seller pays tax on commission, else that tax is irrelevant.

The tax on the commission is $tcs$. So the total selling costs are $cs+tcs$.

We sold the house for $s$, so the amount of money we have after paying commission and tax is $s-cs-tcs$. This should be equal to $pa$. We have arrived at the equation $$pa=s-cs-tcs.$$

We solve this for $s$. Note that the right-hand side is equal to $s(1-c-tc)$. So we are solving the equation $$s(1-c-tc)=pa.$$ Divide both sides by $1-c-tc$. We conclude that $$s=\frac{pa}{1-c-tc}.$$

Note: The numbers should be expressed in decimal form. If we use the numbers of your example, then $p=0.90$, $c=0.02$, and $t=0.13$. As a check of whether you are inputting numbers into the formula correctly, with the numbers you gave I get a selling price of $92081.03$.

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Beautiful. Using s*1 to pull s out of the equation was a huge sticking point for me. For anyone re-reading this pa is percent times asking price so in my example .90 * 100,000. Thank you for an elegant solution. I'm sure I can derive the answer to my additional question from this. –  jamesrward Nov 28 '12 at 7:05

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