My workhorse 4.5" grinder is an older Metabo, made in Germany. If that can't get the job done, I then break out the 9" US made Milwaukee. Both of those will set you back more than your budget.
As a short term fill in, hit Harbor Freight, and go looking for this particular part number 4.5" angle grinder. You need to find a #91223.
Yes, it has less than half the power of my old Metabo, but I won't take the Metabo to work any more. But it has a couple of things going for it.
1] It's on sale for $21.99 till the end of the month. If you have a super coupon, you can get it for even less.
2] If you don't force the issue, and let it take its time making the cut, it does a fairly decent job of it. The spindle nut wrench leaves a lot to be desired, and you're going to want to clean out the grease in the gear case and reload it with something decent (only refill with approx. the same amount though). Other than that, this model seems to be fairly reliable.
I've owned 5 of them over the last 15 year's or so: the first one died when a now former coworker decided to do a durability test on it because I had loaned out to someone I trusted (long story). The next one died under the wheels of a forklift (again, long story).
The last batch I bought two years ago for a temp/ contract welding job ( while I looked for a permanent job). I've worked for the guy off and on for over twenty year's; in his latest start up, he needed to have 15 machine bases welded up in 10 working day's.
They only had one 4.5" grinder: day one said that I couldn't wait for everyone else to get done with it if I was going to get paid. Went and bought three of them (one grinding disk, one sanding pad,one for spare).
At the end of the job, the owner bought the two active one's from me for list price. That's why I only have the one I used in my new job until Milwaukee's went on sale and they stocked up (Haleua!!!!!!!)....?....