I agree that you should pay the same amount.

It feels as though you should be willing to pay twice as much in case 2, since you remove twice as much "death mass". At this point, one might be confused by the apparent contradiction. Some are chalking it up to intuition being wrong (and the problem being misinformed) and others are rejecting the argument. But both seem clearly correct to me. And the resolution is simple - notice that your money is worth half as much in case 1, since you are living half as often!