Is there a FREE Sales Tax Computation API for U.S.A?

I just finished developing an e-commerce iOS app. But I need to have the tax + cart items to be computed inside the app. The app is currently targeting the FLORIDA state of the U.S, but eventually the whole country.

I'm searching for a free sales tax API for this project. For example, I got an item that costs $9.99, and the I live in the CLAY COUNTY with Zip Code 32003 and with a rate of 0.07. (according to the sales tax table I downloaded from: http://ift.tt/2aHCLqc)

The total that I need to pay inclusive of tax would be: $10.69

In the API, I will just pass the tax-exclusive price: $9.99 and the Zip Code, then the API will compute the taxed price for me, which would be $10.69

Or is there an API where I can get a sales tax rate by passing a ZIP Code or address of the user?

Lastly, am I thinking this right? I mean, the way I will compute the taxed price, is this the correct way? Thank you!