The rupee depreciated by 31 paise to trade at a more than four month low of 53.72 rupees against the dollar in early trade on the Interbank Foreign Exchange market today due to increased demand for the American currency from importers.The rupee had lost a hefty 45 paise to close at a four-and-a-half-month low of 53.42 rupees against the US currency yesterday, owing to strong dollar demand from importers amid weak equities.