Praise be to Allah.
If someone rents a house and the contract is signed between him and the owner of the house, then the money paid as rent is regarded as now belonging to the owner of the house from the time the contact was signed, if he allows the tenant to make use of the property (that is, he lets him move in and live in the house). Thus the rent money becomes a debt that is owed by the tenant to the owner of the house.
Ibn Qudaamah (may Allah have mercy on him) said in al-Kaafi (1/279): If [the landlord] rents out his house for a certain number of years in return for an agreed sum of money, that amount of money becomes his from the time he signs the contract with the tenant; it becomes subject to zakaah after one year has passed, and it comes under the rulings on debt. End quote.
Based on that, once the rent becomes due as a result of signing the contract, it becomes a debt owed by the tenant, so it is not permissible for the owner of the house to stipulate that the tenant must pay interest or any additional amount in the event of his delaying payment beyond the deadline, because this comes under the heading of riba, which is haram.
If the contract includes a condition stipulating payment of a penalty in the event of late payment of debt, this is a haram contract and it is not permissible to enter into it, even if the individual is certain that he is able to pay on time, because that is approving of riba and making a commitment to it, which is haram. Moreover, something may happen to him that prevents him from making the payment, such as illness, travel and the like.
For more information, please see the answer to question no. 101384 .
And Allah knows best.