You might have to buy a cheap throw away card. There are way too many people going after the "good" mining cards right now.
Is a basic card, it is $70+shipping Verify that the 4k support is good enough for your monitor. The refresh rate may not be good enough it claims to only do 30hz at full 4k on one of the ports
The important things on the above card to look for are nvidia 710/730 and GDDR5 that is I think the lowest card that does 4k but only at 30hz, and that card sucks for mining I believe so is still in stock.
And it only has 3 ports and one is a vga so 2 of the ports I believe do not support your monitors resolution but will do 1080. It is not a great gaming card, but if not gaming and/or doing lots of 3d work it should be good enough.