Rupee opened on a muted note and fell to an all-time low of 83.72 against the US dollar on Thursday, dragged down by the strength of the American currency in the overseas market and significant foreign fund outflows. Forex traders said the fall in the domestic unit came on the heels of a significant downturn in the Indian equity markets, sparked by the government's decision to hike the tax rate on capital gains. At the interbank foreign exchange market, the local unit was trading in a narrow range. It opened at an all-time low of 83.72 against the American currency, registering a fall of 1 paisa from its previous close. On Wednesday, the rupee depreciated 2 paise to hit its all-time closing low of 83.71 against the US dollar. The government's decision to hike the tax rate on capital gains dampened market sentiment, exerting immense pressure on the rupee and the equity market. "Post-budget day, the benchmark Indian equity indices, BSE Sensex and Nifty 50, dipped by approximately 0.