I read a long time ago that the motivation for funding Columbus' trip had to do with projections showing that at the contemporary conversion rate in Asia would have the Muslim population in the world outnumbering Christians by the time the world would end (which was projected then as somewhere around 1585), and that if Muslims outnumbered Christians then, the rapture would not go well.
Is there any truth to this, and where are good sources to corroborate or dispel the idea? In particular, is there a good trail to follow quantifying the influence that belief in a second coming influenced Spanish (or other European) politics at that time?
Most of my knowledge in this area comes from Karen Armstrong's "The Battle For God: A History of Fundamentalism". Obviously we can never truly know the minds of historical figures.
"The Rapture" is a modern concept that did not exist in the pre-Reformation Catholicism of the 1490s. It has roots in Christian theology beginning in the 1500s, but doesn't really solidify and become a popular concept until North American Evangelical Protestant Christianity really takes off in the mid-1700s.
Because of this, I think it is highly unlikely that anyone in Ferdinand and Isabella's court was counting Asian conversion rates (where would the be getting these figures anyway?) and trying to move chess pieces around to make sure that Christians "win" the Rapture (which wasn't yet a theological concept).
I think what is far more likely is that in 1492 the Spanish government has finally expelled the Islamic Moors from southern Spain. The Inquisition was in full force, forcibly converting remaining Muslims and Jews or expelling them from the country. The end of this war also freed up a lot of money which could then be used for purely financial investments. The Columbus expedition was such an investment.
The Iberian Peninsula in 1492 was a place wracked with religious conflict between Christians, Muslims, and Jews, possibly more so than and other place and time in the history of the West. The end of this conflict meant that money that had been earmarked for the war could be diverted into peacetime investments. While religious motivations colored the Columbus expeditions, I doubt that they were the primary motivation. Even if religious evangelism played a significant role in the funding of Columbus' voyage, the theological concepts of the "end-time" among Spanish Catholics during the 1490s were very different from the American Protestants who coined the term "The Rapture" hundreds of years later.