The US financial behemoth's action comes on the heels of lending rate cuts by its domestic peers like SBI, ICICI Bank and HDFC Bank.
The new rate, effective July 1, makes it the most competitive one among large lenders.
At 9.35 per cent, the base rate is significantly lower than 9.7 per cent offered by SBI, ICICI Bank and HDFC Bank. Axis Bank's offer comes at 9.85 per cent, which it announced last week.
Since January this year, RBI has reduced the repo rate, at which it lends funds to banks, by 75 basis points but banks have passed only around 30 bps to customers so far.
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SBI was the first off the block to lower base rate earlier this month (by 15 bps) after RBI Governor Raghuram Rajan, in the June 2 policy meet, asked banks to pass on the benefit to consumers.
HDFC Bank followed suit with a similar 0.15 per cent cut to 9.7 per cent and ICICI Bank brought down its rate by a marginal 0.05 per cent last week.