I'm not sure that 30 days notice is all that's required to terminate a 1-year lease.
Missouri landlord-tenant statutes provide for tenancies of two different terms: one year and one month. If you have a 1-year lease, it seems to me that you have a 1-year tenancy (payable in monthly installments) and therefore have to give a 60-day notice.
"MO Rev Stat § 441.050.
Tenancy from year to year, how terminated.
441.050. Either party may terminate a tenancy from year to year by giving notice, in writing, of his intention to terminate the same, not less than sixty days next before the end of the year. "
On the other hand, if it is a month-to-month tenancy, the following section seems to make it clear that your tenancy ends at the "periodic rent-paying date":
"MO Rev Stat § 441.060.
Tenancy at will, sufferance, month to month, how terminated--judgment of eviction, how effectuated, landlord's liability.
441.060. 1. A tenancy at will or by sufferance, or for less than one year, may be terminated by the person entitled to the possession by giving one month's notice, in writing, to the person in possession, requiring the person in possession to vacate the premises.
...
4. (1) Except as provided in subdivision (2), the landlord or the tenant may terminate a month-to-month tenancy by a written notice given to the other party stating that the tenancy shall terminate upon a periodic rent-paying date not less than one month after the receipt of the notice.
..."
So, if your "periodic rent-paying date" is the end of the month, you have a legally defensible position, it seems to me.