At the Interbank Foreign Exchange, the value of rupee softens up by 5 paise to trade at 64.39 against the US dollar.
According to the forex dealers said, "Fresh demand for the US currency from banks and importers weighed on the rupee sentiment."
"Domestic equity markets opening with strong gains, however, helped the rupee cap losses", they added.
Meanwhile, the benchmark BSE Sensex hit a new high of 32,374.30 by rising by 128.43 pts.
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