Is it permissible to agree with a merchant to deposit a sum of money with him, and then receive a monthly amount representing my share of the capital after deducting his share of the profits in exchange for his trading activities?

What you have done is Mudarabah (commenda), which is when a person gives money to another to trade with, and the investor receives a specific, undivided share of the profit, such as half or a quarter. It is not permissible to stipulate a fixed amount of profit for either party.

One of the conditions for its validity is that the Mudarib (the working partner) does not guarantee the capital. If a loss occurs, the رب المال (owner of the capital) alone bears it, while the Mudarib bears the loss of his effort.

Therefore, the agreement with the merchant for a fixed monthly amount in exchange for his investment of the money is a loan with an increment, which is haram.