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?
Best Answer
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: $$s=(\texttt{price}(1+\texttt{profit margin})+20)/.75= 1120/(.75) = \$1493.34$$