While what  you write is a reasonable and logical interpretation, it does not necessarily have to be the case. You need to reference the length of the contract as well. If the contract is for a one-year rental, then it would almost certainly be a weekly payment; but if it were a 6 month rental, you'd be making 2 payments per week, or if a two-year rent, you'd be paying twice a month, etc. A contract  must be interpreted in light of all its terms, conditions, entire duration, etc.--you can't look at one isolated provision to understand it.