If you have a Displayport - you can just use this adapter cable to connect your pc to your monitor. -> https://www.amazon.com/Amazon-Basics-Uni-Directional-DisplayPort-Display/dp/B015OW3M1W/
Chromecast plugs into an HDMI, but that shouldn't be an issue. I use this cable on my home rig and at my company all the time with no issues: https://www.amazon.com/AmazonBasics-DisplayPort-HDMI-Cable-Feet/dp/B015OW3M1W/
You'd obviously need the HDMI end to be female, but there are definitely adapters. Something like this would probably be fine: https://www.amazon.com/DisplayPort-Adapter-Converter-Gold-Plated-Compatible/dp/B017Q8ZVWK/
Base level Chromecast is $35, so you'd be under $45 for the whole set up. I doubt you'll find anything else that is significantly cheaper out there.
I had this problem recently. Picked a HDMI to Display Port cable off of Amazon. DP end into my graphics card and the HDMI end into the monitor.
Cable: AmazonBasics DisplayPort to HDMI Cable - 6 Feet https://www.amazon.com/dp/B015OW3M1W/ref=cm_sw_r_cp_apa_i_4XTgBb88N47FG
Edit: included link
Cannot you go HDMI (from mini) to displayport on monitor?
https://www.amazon.com/Amazon-Basics-Uni-Directional-DisplayPort-Display/dp/B015OW3M1W
Does the monitor not have other ports? They usually have multiple ports... Else, get a DP to HDMI cable.https://www.amazon.com/Amazon-Basics-Uni-Directional-DisplayPort-Display/dp/B015OW3M1W
is 10 dollars overpriced? amazon link
undoubtedly it will if purchased from "best buy". lol
A single port can only drive a single display. The DP ports on that (and nearly anything these days) are actually DP++ which means you can use a passive adapter like this for HDMI - https://www.amazon.com/Amazon-Basics-Uni-Directional-DisplayPort-Display/dp/B015OW3M1W
Just buy something like this, no need to overcomplicate it by also having an adapter in the middle of things.