I print almost everything using grayscale. I probably could have bought a B+W printer but didn’t think of it at the time. Considering the expense of the colored ink cartridges, am I saving money in the long run by using grayscale?
You aren’t saving any money unless your printer has a specific black cartridge. Color ink tends to be a little more expensive than black and white ink generally speaking. My printer has 4 cartridges: black, magenta, bluish, and yellowish. The black cartridge is twice as large as the other three colours and costs roughly half as much as any other single color.
My previous color printer had one cartridge for everything color/black and white. It had an option of trading out the color cartridge for a simple black and white one. I did this most of the time as it was much cheaper.
Black ink OK but white ink must be the most expensive of all as I don’t even see it in the computer stores - I bet it must be custom ordered. (sorry couldn;t resist 
)
But yes you are saving money if:
You printer is not mixing colors to get grey (it will look slightly greenish if you are mixing)
And
Your color cartrages get some use so it doesn’t dry out (unless you never plan to use color.