The Indian rupee is staying within a bounded range near record low levels in opening trades on Monday as dollar recovered appetite and local equities stay muted. INR opened at Rs 88.75 per dollar and eased to a low of 88.77 so far during the day. The local unit on Friday extended downtrend to depreciate by 7 paise to close at 88.78 against the US dollar. The USD/INR pair is hovering around its all-time low level, weighed down by trade tensions and global uncertainties. Moreover, persistent foreign fund outflows and the ongoing US visa fee hike issue also dragged down the domestic unit. Meanwhile domestic shares ended modestly higher on Friday, tracking firm cues from global markets amid renewed optimism around artificial intelligence and hopes for more Federal Reserve interest-rate cuts. The benchmark BSE Sensex added 223.86 points, or 0.28 percent, to 81,207.17, extending sharp gains from the previous session after the RBI held the repo rate unchanged at 5.5 percent, lowered its inflation forecast and raised growth projections on Friday. The broader NSE Nifty index rose 57.95 points, or 0.23 percent, to 24,894.25.