# Net selling price with commission and taxes based on percentage desired

Say I have listed my house for sale for $100,000 and I would like to net 90% of my asking price. I have to pay a 2% commission to the buying agent and that commission will be taxed at 13%. How do I calculate this? Also how does the calculation change if the full sale price is taxed and not just the 2% commission. If s is my selling price, a is my original asking price, p is my desired net percentage, c is my commission rate, and t is the tax rate on my commission then I think it should be something like: s=pa+(cts) But I don't see how I can reduce this to a reusable equation where I can just plug in the variables and get s. - ## 1 Answer Let$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