Suppose someone takes out a home improvement loan for $30,000. the annual interest on the loan is 6% and is compounded monthly. the monthly payment is $600. let an denote the amount owed at the end of the nth month. the payments start in the first month and are due the last day of every month. (a) give a recurrence relation for an. don't forget the base case.

Google started as one of many internet search engines, amazon started as an online book seller, and ebay began as a site where people could sell used personal items in auctions. these firms have grown to be so large and dominant that they are facing antitrust scrutiny from competition regulators in the us and elsewhere. did these online giants grow by fairly beating competition, or did they use unfair advantages? are there any clouds on the horizon for these firms -- could they face diseconomies of scale or diseconomies of scope as they continue to grow? if so, what factors may limit their continued growth?