To remunerate is to pay for goods, services, or losses. The word’s root is related to money (hence mune), not number.1 Renumerate is a common misspelling. At least one dictionary lists the latter as an actual word meaning to recount, but in every instance that we can find, renumerate is just a misspelling of remunerate.2

The suggestion was to remunerate teachers more on a personal basis related to individual contribution. [Lawrence Journal World]

The wage cut backfired—Fidesz found it hard to secure appropriate candidates to the rate-council partly because of the low remuneration on offer. [Wall Street Journal]

His 2010 remuneration package included €34000 in benefit-in-kind payments and €4000 for “other remuneration”. [Irish Times]