The rupee fell 2 paise to an all-time low of 84.13 against the US dollar in early trade on Tuesday, as persistent foreign fund outflows and a muted trend in domestic equities dented investor sentiments. Forex traders said all eyes are on the US as it decides its next President. Markets are bracing for potential volatility over the coming days, especially with the Federal Reserve's monetary policy announcement also scheduled this week. At the interbank foreign exchange, the rupee opened at 84.13 against the greenback, registering a fall of 2 paise over its previous close. On Monday, the rupee fell 4 paise to settle at a record low level of 84.11 against the US dollar. The rupee closed at an all-time low on Monday and opened at a new low of 84.13 as US elections rattled stock markets amid persistent foreign fund outflows, said Anil Kumar Bhansali, Head of Treasury and Executive Director at Finrex Treasury Advisors LLP. "The Reserve Bank of India (RBI) was present to absorb the fall