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MEXICO CITY, Aug 4 (Reuters) - Mexico’s peso firmed to a six-year high on Monday as lower oil prices eased some economic fears and investors bet on higher local interest rates, while stocks sank to a six-month low.

The peso MXN=MEX01 gained 0.9 percent at the central bank's final 1:30 p.m. (1830 GMT) reference to 9.8745 per dollar, its strongest since late August 2002.

The benchmark IPC stock index .MXX closed 1.75 percent lower at 26,487.76 as falling commodity prices hit Mexican miners and fears of further losses at banks knocked down stock markets around the world.

“There is a lot of nervousness that banks will keep seeing their balance sheets deteriorate,” said Mauricio Brocado, an analyst at Actinver brokerage.

However, the peso reacted to a sharp drop in oil prices CLc1 that tempered worries that high fuel costs could further crimp consumer spending in the United States, the destination for around 80 percent of Mexican exports.

“Lower oil prices will reactivate the economy, especially the American economy, which in the end will be good for Mexico,” said Francisco Diez, head of emerging markets trading at RBC in Toronto.

The peso last Friday broke past 10 pesos per dollar for the first time since late 2002 on expectations that Mexico’s central bank will further tighten borrowing costs to battle a spike in inflation.

That would further widen the spread between benchmark U.S. and Mexican interest rates and make peso-denominated assets more attractive to investors.

Last month’s second consecutive hike by Mexico’s central bank of its key overnight rate to 8 percent pushed the spread to 6 percentage points, the widest since late 2005.

The peso has gained 4.6 percent against the dollar since June when the central bank began to tighten borrowing costs and the currency is up more than 10 percent for the year.

In debt trading, the government's benchmark 10-year peso bond MX10YT=RR rose 0.534 of a point in price to bid 93.081, pushing its yield down 9 basis points to 8.84 percent.

In stock trading, shares of America Movil AMXL.MX, Latin America's biggest cell phone operator, lost 1.61 percent to 24.40 pesos while its New York shares AMX.N fell 1.02 percent to $49.41.

Shares of copper miner Grupo Mexico GMEXICOB.MX fell 5.68 percent to 15.95 pesos as futures prices for the metal plunged to a six-month low on fears of slowing global demand.

Miner Penoles PENOLES.MX shed 8.06 percent to 241.03 pesos. (Reporting by Michael O'Boyle; Editing by Leslie Adler)