Does Mojave make old MacBook slower?
I have a 2013 MBP running Mojave. It’s showing no issues and works fine. No concerns on speed. I noted no apparent slowdown in anything after upgrading from High Sierra. I think you should be fine... I wouldn’t even consider a 2016 model to be “old” at this point.

A sided by side comparison shows Mojave actually been slightly faster overall, and much faster in Booting.

Reboot average times were 212 seconds in High Sierra but only 124 seconds in Mojave, that’s an 88-second improvement.

However, as with any new OS X, the performances from 3D party apps might be initially impacted till they provide updates to they products. 

Example Adobe CS Premiere Pro is 2 seconds slower in opeing on Mojave.

Do not have "word processing apps" to compare to answers your question.