Let's assume you spend 30% of your time sleeping (7.2 hours a day), and your expected lifetime to be T. Then your "useful time" is 0.7T. So you decide to sleep

Let's assume you spend 30% of your time sleeping (7.2 hours a day), and your expected lifetime to be T. Then your "useful time" is 0.7T. So you decide to sleep 25% more (9 hours), so you sleep through 37,5% of a day and your life expectancy is now T'=1.25T, so your useful time is 0.625T'=0.625 x 1.25T=0.781T. Your useful time grown around 12%. Note that if you take your working hours into account and you are only interested in your free time after work, then this free time will hoard up more at the end of your life when you will be retired but you will lose free time before that.