How much is a 'perutah' worth in modern currency?
I believe for most Halachic topics today that require "one prutah's worth" of cash, goods, or services (e.g. the minimum needed to effect a wedding), we go with an economic definition: the smallest amount of money that can buy something. Despite inflation, there are plenty of things you can still buy today for fifty cents or less, so fifty cents is certainly shaveh prutah; I'm not sure whether it's a nickel, dime, or quarter, but fifty cents certainly is enough. Or as someone once said to my father:
You mean instead of a gold ring, a guy could march down the aisle and give the bride the little metal tab off his soda can?
My father replied:
No, that's not nearly enough. He'd have to give her the entire can of soda.
The weight of a p'ruta was half that of a barleycorn, and it was silver. Assuming — without justification — that barleycorns weigh now what they did then, and other unjustified assumptions, we have: Wikipedia gives the weight of a barleycorn as about 65 mg. At about 31,103.4768 mg per troy ounce and a current price of silver of about USD28.20, that gives about 2.9 cents to a p'ruta.
Rav Moshe Heinemann writes in multiple places over the last couple of years (2018-2020) that he believes a peruta is about ten cents.
There should be a פרוטה for every person the Rav represents. I believe a פרוטה is about 10 cents today. Rav Moshe writes if you can’t buy anything with a penny, then it’s not considered a פרוטה . Even bubble gum balls are more than a nickel. Therefore, if you represent 1,000 people, you need at least $100 which the non-Jew would give to the Rav selling the chametz. Moreover, the Rav needs to receive another פרוטה for every person represented if he plans to sell the place of the chametz too.
The Rambam says the value of a peruta is a חֲצִי שְּעוֹרָה של כ סף – half the size of a barley kernel made of pure silver. How much is that worth? It fluctuates daily. Most silver sold today is sterling silver which is .925 silver, which is not 100% silver. The reason for that is the same reason why we use 14 karat gold for a ring rather than pure 24 karat gold. Gold is a soft metal, so if you press down on the ring then it will get bent out of shape. Therefore, they mix the gold with nickel or other metal which stiffens the gold. That’s why gold rings are only .585 or 14 karat gold, while the rest of it is some other metal. Pure silver is much more expensive than just another 110 above sterling silver. They have to purify the silver to the point of having no other impurities inside. Still, this value today is worth a few cents. Rav Moshe Feinstein says that a peruta is the smallest coin which still has a value. I remember in the good old days when you could buy two gum chiclets with one cent or weigh yourself for a penny. Now it costs 25 cents to weigh yourself. At one point you could buy a ball of bubble gum for 5 cents, but now it costs ten cents or more. Of course you could buy a one cent postage stamp but you’re essentially trading one penny for another penny which doesn’t mean anything. If you’re fast enough you can also get one cent worth of gasoline, but there’s nothing you can do with that. I believe there is nothing significant that you can buy nowadays for less than ten cents. Therefore, a peruta would require at least ten cents. The Gemara says someone was mekadesh a woman with a date, so they needed to evaluate whether the date was worth a peruta at that time. Based on that, I guess you would need to investigate whether ten cents could buy something if someone uses it for Kiddushin.