People usually move by the end of the month

Depends on what you have.

If it is a condo, you can often find someone by the last minute.

If it is a single family house, then the renters apply a month ahead of time as they need to give the current landlord 30 day in advanced notice.

I would lower the price.

Say it this way-

If the rent is $2000 per month, a one hundred dollar per month is only $1200 for the year. But, a vacancy of one month is $2000.