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I have a math question that is just driving me nuts. I have items that I want to sell on an online platform, however there are a number of fees and taxes involved, but the seller has to be responsible to pay for all these, therefore the final sales price must be inclusive of all these costs.

Lets say i have an item that costs 1000 dollars

  • The profit margin applies to only the cost at 10%
  • The online platform charges a 10% fee on the final sales price collected from the seller
  • The item is subject to a 15% sales tax + a processing fee of 20 dollars.

The problem is that since I need to include all these fees and taxes into the sales price, but every time the sales price goes up, so does the fees and taxes.

What would be the math formula for me to calculate how much I should list the item?

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  • $\begingroup$ First of all, discard the clause "If the 15% sales tax results in an amount lower than 60 dollars...". The cost is 1000 dollars; thus it 15% is at least 150 dollars. $\endgroup$ May 30, 2019 at 13:37
  • $\begingroup$ Okay, im going to remove it. $\endgroup$
    – Cynric Ng
    May 30, 2019 at 13:39
  • $\begingroup$ But the addition of the fees and taxes alters the final sales price, which would affect the fees and taxes in proportion, right? $\endgroup$
    – Cynric Ng
    May 30, 2019 at 13:43
  • $\begingroup$ Since in order to be inclusive, the final sales includes the tax and fees and processing fee by the %. $\endgroup$
    – Cynric Ng
    May 30, 2019 at 13:45
  • $\begingroup$ The thing I can't get my head around is since the tax and the fee is charged on top of the "Final sell price", but in order to be inclusive of all costs into the sell price, the tax and fees which are added result in a higher sell price, which brings me into a loop of resulting in higher tax and fees. $\endgroup$
    – Cynric Ng
    May 30, 2019 at 13:51

1 Answer 1

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Say you sell the item at $s$ then you will receive $s-\texttt{fees}-\texttt{tax}-20=s-.1s-.15s-20=s(.75)-20$. You want this to equal $(\texttt{price})(1+\texttt{profit margin})$. Let's solve for s: $$s=(\texttt{price}(1+\texttt{profit margin})+20)/.75= 1120/(.75) = \$1493.34$$

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  • $\begingroup$ Thank you, yes this answered my question perfectly $\endgroup$
    – Cynric Ng
    May 30, 2019 at 14:23

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