The rupee on Monday closed down by 2 paise at 49.46 against the US currency due to strong dollar demand from importers and weak stock markets. The domestic unit opened lower at 49.61 a dollar from previous close of 49.44.It touched a low of 49.80 in late morning deals in line with sluggish local stocks. The rupee bounced back later to a high of 49.32 on some recovery and later fell back to end at 49.46, still showing a fall of 2 paise.