question about intention to fast

i learned you can make intention to fast once for the whole month so on the third day of ramadan my fast was broken so i learned you can make an intention to fast for the whole month on the 7th day, today on the 8th i told myself i was gonna make intention when i got out of the bathroom but i forgot so is my intention to fast the rest of the days of ramadan from the 7th also suffice for the lack of intention on the 8th?