Traveling Abroad

There are so many existing insurance companies nowadays and more accidents that happen every minute. We cannot predict what happens to us, when and where it will happen, especially nowadays that people are always travelling and are always in the move. But what if one suddenly gets into an accident somewhere in Jakarta, Indonesia, Brunei or Singapore and your insurance company is in the states? Will you still be covered? Or will you just be left rotten inside a strange hospital with strange people around you and mountain of bills to pay?