As trulib said, it’s not profit in the sense you’re thinking of. Interest is profit when regarding capital.
IN other words.
I can choose to buy a widget today at $100, or I can choose to buy a claim on a widget next year at $80. If I am allowed to place a claim on a future widget, I may buy it today for $80. In one year it will mature to a greater value of $100+. I could then sell it, or consume it, but either way I made a 20% profit/interest.
Marx thought that Interest was the amount of money skimmed off the top by the capitalists from the total revenue generated by the “laborers”. Marx’s argument is that for laborer’s to receive their full pay there would be no interest as the laborers would receive full value for everything and nothing would be left over for the capitalist.
What Böhm-Bawerk is showing is that interest is not the result of exploitation of the laborer. Interest does not form from any type of exploitation of the laborers but instead is a naturally occurring phenomena that happens with regard to time, and the desirability of present consumption to future consumption. The rule of thumb here is that in general people tend to prefer present goods to future, and that there is a price discount for the consumption of future goods.Interest reveals a discrepancy regarding the consumption of present to future goods. So what he is saying is that it’s entirely non-sequitir to state that interest occurs due to the exploitation of labor workers, who don’t receive full value of their end product as interest occurs naturally across many things, not just capital alone. Interest is the result of the capitalist paying now for a future good, and the discrepancy of price there-in. Other parts of the argument aside, Interest is a naturally occurring phenomena, and it has nothing to do with exploitation and everything to do with the subjective preferences of individuals regarding consumption over time.
Böhm-Bawerk will also go on to explain, agreeing with Marx, that the laborer should receive full value for the efforts placed into creating the end product. He just goes to show that the full value of the laborer’s input does not equal the full total value of the end product, but a portion of it and its total calculated worth is done at the present(not the future). With this he also goes on to show that the laborer must decide whether to get paid today, in wages, or wait possibly years before the final product matures in value and is sold. If the laborer gets paid in today’s wages he’s going to get paid for his value in today’s market at today’s rate(Before the maturity of their final investment matures). The only way the laborer can ALSO earn interest on his labor is if he chooses not to get paid for the duration of the production process and receives his reward after the product has been sold(possibly years later). In this case all that’s happened is that the laborer in a way just became one of the capitalists(The laborer saves as opposed to consuming now). The laborer needs a way to live however, so they generally prefer to get paid in wages in the present(today), rather the future(years later).
In most cases the laborer will choose the wages. There is no coercion of any type beyond that of limitations that nature imposes on us, like time and scarcity.
That is an extremely crude explanation, hope it helps.