How to store tax for a Product when tax rate for a Product can change and tax-exempted Products Product

id
name
price


Tax

id
name
rate


Product_Tax

Product.id
Tax.id
effective date
expiry date


Is this a good design? 

How to store Products that are tax-exempted?

Also, how to handle the case when the value of Tax changes for example VAT rate changes from 20% to 30% --> Should I store the value of rate in the Product_Tax table in that case
Don't put tax exempt entries in the Product_Tax table.

Design is good (already endorced by me).