OP:
What kind of a budget do you have for a replacement?
Knowing "the numbers" would help with a suggestion.
If you need more current OS software, I'd suggest using one of "dosdude1's" patchers:
This has a tool built right in that downloads Mojave (look in the "Tools" menu).
You use that to create a bootable USB flashdrive.
I recommend using "Install Disk Creator" (free) to make it.
Then boot from the flash drive.
Erase the iMac internal drive (MAKE SURE YOU ARE BACKED UP FIRST, shouting is intentional)
Install new OS.
Restore your data from the backup.
This should get you "far enough" so that you can use a more modern browser with which to interact with your online banks, etc.
Sooner or later, however, you must face the reality that you can only "go so far" with an older computer, and that something newer is required.
Hence, why I asked about a budget above.
Aside:
OP seems to have disappeared, I think we scared him off...