In the middle of nowhere there have been quite a number of land sales with $10k+/acre in the past handful of years.
Farmland prices have been kinda crazy over the last 5-10 years.
As a quick example of some math:
* Rent prices for farmland in Iowa [1] averaged $230/acre in 2016
* Yield per acre for corn is 203 in 2016
* Price per bushel averaged $9.27 [3]
Throwing averages into the mix, $1,882 revenue per acre. Without any expenses, farmers could be looking at >5 year time to break even at a 10k purchase price as opposed. Tons of farmers are paper millionaires simply because of the land they own. 100 acres of 10k land gets you there. 640 acres is 1 square mile (much of the state is on a 1x1 mile grid of gravel roads).
And of course I found most of the work already done after I found a bunch of sources. [4] has some more detailed numbers.
[1] http://dreamdirt.com/blog/2017-iowa-farmland-cash-rent-rates...
[2] https://www.extension.iastate.edu/agdm/crops/pdf/a1-12.pdf
[3] https://www.extension.iastate.edu/agdm/crops/pdf/a2-11.pdf
[4] https://www.extension.iastate.edu/agdm/crops/pdf/a1-20.pdf