THE median price of a house rose to a record NZ$142,000 (HK$710,525) in October, exceeding the previous record of $141,000 set a month earlier, said the Real Estate Institute of New Zealand. The total value of the 7,787 homes sold was $1.34 billion, up from 7,326 homes sold for almost $1.25 billion in September. In October 1994, the institute said a total of 7,708 homes were sold at a median price of $135,000. Institute President Kent Prior said the price rise in October partly reflects competition among banks in mortgage lending. Mr Prior said the latest round of mortgage rate cuts and further falls anticipated for the New Year are having a positive effect on the housing market. Of the homes sold in October, 291 were priced at more than $400,000.