The rupee opened on a flat note and rose 1 paisa to 84.07 against the US dollar in initial deals on Thursday, as strong dollar and persistent foreign fund outflows dented investor sentiments. Forex traders said the rupee remained range bound as month-end demand kept the US dollar well-bid. Moreover, a muted trend in domestic equities weighed on the local unit, while any intervention by the Reserve Bank of India (RBI) may support the local currency at lower levels, they said. At the interbank foreign exchange, the rupee opened at 84.08 against the greenback, it rose 1 paisa to 84.07 in initial trade. On Wednesday, the rupee depreciated 3 paise to close at 84.08 against US dollar. The local currency has been hovering around its all-time low level. Rupee touched its lowest closing level of 84.10 against the dollar on October 11. The rupee has been trading below the 84-level for the majority of October, but the recent pressure is primarily due to domestic factors, notably month-end d