1

I, a vendor, need to find the sales tax from a tax included price that does NOT apply tax to the portion of the total that IS tax. Most answers result in overpayment of taxes.

Please do not tell me this: receipts from items subject to sales tax, divide the receipts by 1 + the sales tax rate. For example, if the sales tax rate is 6%, divide the total amount of receipts by 1.06. If the sales tax rate is 7.25%, divide the total receipts by 1.0725. Variations of this formula are provided everywhere I search and it is incorrect/incomplete for this situation.

Problem with this above answer: I am using my wholesale rate, NOT a sale + tax total. If I use the above formula, I will pay taxes on each of the three components of the price 1) wholesale cost 2) my markup or profit and 3) the local tax amount, all of which are a part of the tax included sale price. This means that I am paying tax on the tax. Is there an algebraic solution? Thank you for your consideration.

user3648099
  • 11
  • 1
    I do not understand your problem. Can you give a numeric example of correct input and output. (You may want to start from the nat price without tax, add tax in the obvious manner and thus obtain the tax included price if you prefer) – Hagen von Eitzen May 17 '14 at 18:18
  • Also to clarify: You are talking about sales tax, not value added tax? – Hagen von Eitzen May 17 '14 at 18:22
  • Additional info...yes, this is sales tax. Suggested retail price – user3648099 May 17 '14 at 18:55
  • Yes-sales tax. Suggested retail price=60.00, tax rate= 6.75% Normal method of pricing is to take price +(price x.0675) for out-the-door price. Tax included price is a little more difficult. Consider that same $60. 60 x .0675=4.05. The customer only paid $60 as a tax included price. So as the vendor, I pay the $4.05 from the purchase price of $60. The problem is that I should subtract the tax from the price (60-4.05=55.95) Now I am calculating the tax from this price so that I don't have to pay tax on the tax. If I take 55.95 x .0675 = 3.78 (rounding up). 55.95 + 3.78=59.73 (this off 27 cents) – user3648099 May 17 '14 at 19:09

1 Answers1

0

short answer: multiply the tax included price by $.063231850$ to calculate the tax you should charge- this gives you $3.79.$

$.06323185$ is equal to the tax rate divided by $(1$ + tax rate) or $\dfrac{.0675}{1.0675}$

Another way to view this problem is to break it up into pieces.

1) untaxed price
2) markup
3) combined price plus tax
4) subtract out 60 that the customer has already paid.

The first step IS to divide the customer price (which includes tax) by $1.0675$ to get the original untaxed price.

Add your markup to this untaxed price to get a subtotal.

Multiply this subtotal by the tax rate of $1.0675$ to get the tax amount.

Add the tax amount to the subtotal to get a total price.

Subtract out $60.00$ since the customer has already paid it.

Hope this helps.

Regards,

Laine

homegrown
  • 3,678
Math Teacher
  • 26