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The four-day forwards, which were actively traded, closed at 131.99/132.05 per dollar.
The three-day forwards, or spot-next, started to trade on Monday around 131.99 per dollar level.
The spot currency was not traded after the central bank capped the currency at predetermined levels to prevent volatility, traders said.
Central bank Governor Ajith Nivard Cabraal said on Thursday that the rupee would be stable during this month.
Overseas investors sold a net 367 million rupees worth of government securities during the week that ended December 17.