If (annual) inflation is 40%, then the annual discount factor is 1.40 and the monthly one is c = 1.40^(1/12) ≈ 1.0284.

Assuming the $100 payments are paid at the end of each month, the value of the money sent over in today's dollars is $((100/c^1) + (100/c^2) + (100/c^3) + ... + (100/c^12)) which is a geometric series with ratio 1/c, so the sum is (100/c^1 - 100/c^(12+1))/(1-1/c) ≈ $1005.

So take the cash offer.

For spreadsheet calculations, look into the SERIESSUM flavor of macros.

That's computing based on purely the discounted value of money. The more useful metric is not the % of inflation, but rather the % you can get on your money lying around (your answer assumes that to be 40% annually as well - i.e. a real rate of zero, but real rates on all of your options could be deeply negative as well).

(though from an academic point of view you are completely correct)

Are they monthly payments?

Yes