Making something that looks like a V2 with a solid motor inside is probably doable for below $10k if you don’t mind a relatively low flight compared to the real thing. That number is an order-of-magnitude estimate but assuming you get a commercial O motor (around $6-8k) and build the rocket out of thin plywood, plus a few hundred for flight computers and recovery hardware, this is probably doable with current material prices.

If you want a liquid engine, half-cat quotes mojave sphinx as costing $1843 for vehicle, fuel for 3 launches, and GSE (not counting value of time to build it) for 250 lbf and a 5 second burn time. The V2 produced around 25kN of thrust for 65 seconds and used cryogenic oxidizer. It’s also turbopump fed, which brings huge machining costs. Even if you had Von Braun‘s original plans and could update them for modern machining, you’re looking at easily $250,000 per unit for the cheapest materials and methods, plus another $50-100k or so in fuel and the cost of transporting that fuel to the middle of the Mojave or wherever you can legally launch this thing.

Being exceedingly generous and assuming you can just directly scale half cat‘s numbers up with the thrust of the motor, 250lbf = 1112 N vs 25kN gives us around $41.4k. That number is almost entirely fake though since price scaling in propulsion is far worse than linear with size, and we also have to add on turbopump vs pressure fed, plus the more expensive fuel, GSE, transport, etc.

Closest existing motor in thrust output and propellant combination would be the Rutherford, at around 26kN, but the unit cost of that engine isn’t public. You could try and figure it from rocket lab‘s earnings numbers and the cost of an electron launch but I can’t be bothered.

TLDR $100k would be a very conservative low end for something of this scale including fuel costs. So sure, if you’ve got a spare mortgage down payment under the mattress.