Are the following sentences both correct and interchangeable?
Teacher assistants will receive a monthly fee for housing.
Teacher assistants will receive monthly fees for housing.
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If teachers are given money to help them pay for rent, this is called a stipend, or (less professionally) an allowance. Stipend is normally singular as teachers are given a single payment to cover all expenses.
Teacher assistants will receive a monthly stipend for housing and related living expenses.
It doesn't matter if the stipend is broken into multiple payments each month. Stipend is still singular.
Teacher assistants will receive a monthly stipend for housing, broken into two payments.
If instead you mean that teachers will have to pay a certain amount each money for housing, then the normal term for this is rent, not fee. Also if you are the person doing the renting you do not receive the rent. You pay it.
Teacher assistants will pay a monthly rent for housing.
They are not quite equivalent. The first sentence implies that a single "fee" will be given to the teacher during the month. However, in the second sentence it implies that the teacher will be given multiple "fees" during the month.
I have more issues with the use of "fee". Usually one pays a fee or one receives a payment.