Mo. Rev. Stat. § 148.160

Every taxpayer shall file a return with the director on or before the fifteenth day of April in each year. The director may grant a reasonable extension of time for filing returns under such rules and regulations as he shall prescribe. Whenever such an extension of time is granted, a taxpayer shall be required to pay as part of any tax due interest thereon at the rate determined by section 32.065 from the day when such return should have been filed if no such extension had been granted.