The way they say it works is that Google sees people investing in long term sites and likes it. When someone registers for only one year, it’s a good chance that they’re just spamming. A ten year lease on a domain is going to show that they plan to stick it out for the long term.
Well guess what? It’s not true. They’re idiots and liars. It doesn’t work that way. I don’t know where they got this “fifteen times faster” thing, but they’re either terribly mistaken or just plain lying.
Understand, Google can’t see that information. It’s between you and your provider. Even if you put that stuff out in the open for the world, and Google, to see, they’re not looking for it. Sure, in the past they’ve said they might take it into consideration, but as of right now, they’re not even looking.
Don’t worry about investing the amount of money needed on a ten year lease, unless you’re comfortable and plan on investing in a ten year lease. Don’t do it because this guy says to, or because your provider says to, do it because you want the domain for ten years.