Moving MS Office 2008 from 12-yr old iMac to new MacBook Air (M1)

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No. Microsoft Office 2008 is 32-bit not compatible with new versions of macOS.

You can either purchase a new license for Microsoft Office, Microsoft Office Home and Student 2021 (One Mac) - Apple, or use Apple's iWork: iWork - Apple.

Jack

It won’t run, it is obsolete. Your files will be compatible with newer versions of Office however. Either purchase a subscription to Microsoft 365, and download Office via the Mac App Store, or grab a copy from a retailer or Microsoft of the 1 time purchase version of Office, Office 2021.

I would recommend Office via the Mac App Store and Microsoft 365 as it gives you the most features and gives you access to the latest version of Office at all times.

No for several reasons:

1. Apple switched from 32-bit apps to 64-bit ages ago.
2. Apps need to be updated for Apple silicon or they eventually won’t continue to work.

At some point, you will need to upgrade.

The time is now. 

You might look at the free, open-source alternatives to MS Office: LibreOffice and SoftMaker FreeOffice 2018.  Both can open, edit and save MS Office files in their original format or their own format.

Why not simply use Apple Pages?

It’s free and your old MS/Word documents should import just fine.

You would have to all upload them. To be honest, I find Word online fiddly, and frustrating. And it’s lacking features, you can’t even insert a textbox!

Can I suggest, what about using the Pages word processor available from Apple. Since you just need the basics, it should do very well. It’s free, and if not already on your Mac, can be downloaded from the Mac App Store. You can convert word files to view and edit them with it. Pages - Apple (UK).

There is also Numbers, and Keynote, which can be likened to Excel and PowerPoint respectively.

As shown here: Export to Word, PDF or another file format in Pages on Mac – Apple Support (UK), you can export to a Word or PDF file from Pages should you need to.