Time Travel Paradox?Suppose I travel 40 Years back in time and then kill my grandfather then will I be alive?

Suppose if I travel 40 years back in time and then kill my grandfather,then will I be alive today(if I again come forward to 40 years (my present time))?Will I exists naturally subject to Laws of Physics. And will be my existence natural? Or is there really a Time Travel Paradox proof by formula of physics. Guys I just watched Morgan Freeman doentary "Through the Wormholes" .