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Forex traders said the broad weakness of the American currency in the overseas market and sustained foreign fund inflows supported the local unit, while high crude oil prices restricted the gains.
At the interbank foreign exchange, the rupee opened at 73.51 against the dollar, then inched higher to 73.45, up 5 paise over its previous close.
On Wednesday, the rupee had settled at 73.50 against the US dollar.
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Foreign institutional investors were net buyers in the capital market on Wednesday as they purchased shares worth Rs 232.84 crore, as per exchange data.
On the domestic equity market front, BSE Sensex was trading 146.4 points or 0.25 per cent higher at 58,869.60, while the broader NSE Nifty advanced 40.85 points or 0.23 per cent to 17,560.30.
Meanwhile, global oil benchmark Brent crude futures rose 0.26 per cent to USD 75.66 per barrel.
On the domestic macro-economic front, the Union Cabinet on Wednesday approved a big-bang relief package for the stressed telecom sector that includes a four-year break for companies from paying statutory dues, permission to share scarce airwaves, change in the definition of revenue on which levies are paid and 100 per cent foreign investment through the automatic route.
The Union Cabinet also approved a revised Rs 25,938 crore production linked incentive (PLI) scheme for auto and auto-components industries to enhance the domestic manufacturing capabilities.
According to experts, these announcements could lead to fund inflows and that may lead to strength in the rupee.