The spectacular rupee turnaround was seen despite highly bullish greenback overseas and steady capital outflows.
Overall forex market sentiment was backed up by the government announced that it will stick to its fiscal deficit target of 3.2 per cent of the GDP.
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On the other side, the US dollar traded broadly higher against its major trading rivals in response to the rising optimism following the tax reform proposal by the Trump administration.
Meanwhile, foreign institutional investors (FIIs) continued their selling spree and offloaded net equity worth Rs 5,328.46 crore yesterday from stock markets yesterday, as per provisional exchange data.
Reversing initial strong buoyancy, equity markets ended on a flat line due to frantic profit-taking at higher levels as investors turned cautious and were unwilling to take heavy bets ahead of a long weekend break.
The benchmark Sensex settled flat at 31,283.72, while Nifty advanced over 19 points to 9,788.60.
At the Interbank Foreign Exchange (forex) market, domestic currency resumed sharply higher at 65.35 against its overnight close of 65.50 on adequate dollar supply.
It strengthened further to touch a fresh intra-day high of 65.2350 in mid-afternoon deals before concluding at 65.28, showing a steep rise of 22 paise, or 0.34 per cent.
On the weekly basis, it has depreciated by a whopping 51 paise.
The RBI, meanwhile, fixed the reference rate for the dollar at 65.3552 and for the euro at 77.0603.
The forex market will remain closed on Monday in view of Gandhi Jayanti.
The dollar index, which measures the greenback's value against a basket of six major currencies, was little changed at 92.95.
In cross-currency trades, the rupee rose further against the pound sterling to settle at 87.39 from 87.95 per pound and hardened against the Japanese yen to end at 58.03 per 100 yens from 58.12.
It also continued to rally against the euro to close at 77.10 from 77.13 yesterday.
In forward market today, premium for dollar eased further owing to sustained receiving from exporters.
The benchmark six-month premium payable in February edged lower to 108.25-110.25 paise from 110-112 paise and the far forward August 2018 contract also declined to 246.75-248.75 paise from 251-253 paise yesterday.
On the international energy front, crude prices traded mixed on Friday, but both Brent and US crude were set to chalk up another weekly gain as investors bet that efforts to cut a global glut are working and that the demand outlook is improving.
Tensions around Iraqi Kurdistan threatened the region's crude supplies, helping Brent prices to their strongest third-quarter performance since 2004.
Brent fell 7 cents to USD 57.34 a barrel, heading for a fifth weekly climb and a more than 9 percent gain for September.
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