At the interbank foreign exchange, the rupee opened at 76.34 against the American dollar, then lost ground to quote at 76.35, registering a fall of 6 paise from the last close.
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On Monday, The rupee depreciated for the third straight session to close 10 paise lower at 76.29 against the US dollar.
The dollar index, which gauges the greenback’s strength against a basket of six currencies, was trading 0.14 per cent higher at 100.92.
The Indian rupee opened weak and is expected to weaken against the US currency this Tuesday as the Federal Reserve interest rate outlook boosted the dollar index to its highest level since March 2020, said Sriram Iyer, Senior Research Analyst at Reliance Securities.
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However, further depreciation could be capped as the RBI could be present to curb volatility, Iyer added.
On the domestic equity market front, the 30-share Sensex was trading 57.03 points or 0.10 per cent lower at 57,109.71, while the broader NSE Nifty declined 3.65 points or 0.20 per cent to 17,170.00.
Global oil benchmark Brent crude futures rose 0.51 per cent to USD 113.74 per barrel.
Foreign institutional investors were net sellers in the capital market on Monday, as they offloaded shares worth Rs 6,387.45 crore, as per stock exchange data.