Twitter's mMAUs (monthly Monetizable Active Users) stands at 450 million. If they pay $8 per month, that gives Elon $3.6B per month. It will take 13 months to make $44B - the purchase price QED. Elon Musk is a genius.
Not everyone will be willing to pay the $8 (trust me, all those blue tick people are capable of paying monthly, but they just won't because they can't stand Elon Musk and hates him just because everyone is hating him), so your calculations are off I guess. Would take more than 13 months. They got to pay to the bills too! So two or more years unless Twitter actually does get more profitable by attracting more users. Since they are going to relaunch vine and also likely to reward content creators, more users might actually join the platform increasing the revenue from ads and sponsorships.