No---sorry---your old Mac does not meet the system requirements for desktop software now. So....if you cannot upgrade your OS, you can still use online software. You cannot use that license key to pay for online TT, though. So....seek a refund from Costco. Or maybe you can get a refund from TT--
https://ttlc.intuit.com/community/system-requirements/help/minimum-system-requirements-for-turbotax-...
To request a refund for a TT product
https://ttlc.intuit.com/turbotax-support/en-us/help-article/intuit-refunds/request-refund-turbotax-p...
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
