If this concept of somebody paying for other's sins does not work in this life how can it work in next life?

A case for Christianity:

Protestant reformer Martin Luther, writing in the spirit of Jesus' statement, taught: "Be a sinner and sin vigorously; but even more vigorously believe and delight in Christ who is victor over sin, death and the world.... It is sufficient that we recognize through the wealth of God's glory the lamb who bears the sins of the world; from this sin does not sever us, even if thousands, thousands of times in one day we should fornicate or murder" (letter to Philip Melanchthon, August 1, 1521). Humorist Jules Feiffer has bitingly satirized Luther's position: "Christ died for our sins. Dare we make his martyrdom meaningless by not committing them?"