Sometimes, tenants want to move into an apartment in the middle of a month, and landlords are happy to go along with this arrangement. This is most likely to happen with an apartment that has been vacant for a while. In this situation, not only is there no need for a new tenant to wait until a current tenant vacates at the end of the month, but the landlord is eager to fill the vacancy and resume collecting rent.
Leases usually begin on the first day of the month, and for good reason. Since rent is paid on a monthly basis, it makes sense to align each rental period with an actual month. As a tenant, you probably prefer thinking in terms of January's rent, February's rent, and the like. Landlords and management companies also prefer this, because it's easier to manage apartments when all the rents are due on the first of each month.
If an apartment you wish to rent will be ready before the first of the month, you and your landlord may agree to start your lease earlier. It follows that you should then owe rent for just part of that first month. This lower rent is called "prorated rent" because it's based on how much you owe per month but it's calculated to reflect the actual portion of the month in which you have possession of the apartment.
When Lease Term Begins Is Key
You should owe prorated rent if you don't have the right to occupy your apartment until some day after the first of the month. So, if you've arranged with your landlord to begin renting your apartment on October 15, for example, your lease should identify October 15 as the beginning of the lease term.
If your lease term begins on the first of the month, but you choose to move in later, you'll still owe rent for the entire month. In this situation, you agreed (when you signed the lease) to pay a full month's rent in return for a full month's use of the apartment. If it turns out you didn't move or didn't begin to use the apartment in earnest until later in the month, you'll have no legal basis for paying prorated rent.