There is no good answer to your question and ......

these "deals" often end up badly. You should expect to hear from her at some point that she needs MORE money from you, or has an "emergency" and needs fast cash.  Most fools get taken advantage of, or ripped off, or get burned in these deals at some point.  You should beware. Also don't expect exclusivity because that won't happen even in the best of circumstances.  If you are going to go through with this you need to be eyes wide open and not taken like a street idiot in a 3 card monty game. I would NOT pay a big sum up front unless you expect to lose it !

 Ask HER what she thinks is fair & then negotiate downward. Do NOT lend money EVER or have her cry to you she needs more and give in. Be smart and think with the big head.

If you are paying her $500 an hour, then the number would be much different than if you are paying her $150 an hour.  

Assuming $300/hour as a basic rate, for the amount of time you want to spend with her, I think you'd be lucky to get this for $2.5K/month.  But, you never know.  When offering a regular deal, she might be willing to go as low as $1500.

Aside from what you pay her now, it also depends on how much she needs the money and how much of a discount it's worth to her to have the steady, in advance, payment.

You'd also want to clarify what kind of priority you would get with scheduling.  I used to pay a few girls for several sessions in advance, on a buy 3 get 1 free kind of deal.  It worked out, occasionally, but also failed occasionally.  One girl started blowing off my attempts to schedule saying she couldn't turn down a session with someone who wanted to pay.  She felt like she was giving me sessions for free, almost forgetting that I had already paid for them.  

It can work, but you have to be resolved to yourself that at some point, it might stop working out, and you may lose money in the deal, and you have to be OK with that.  If she takes your first payment, and then sees you once and never again, call it a life lesson and move on.  Don't do it if it's gonna piss you off and cause you more stress than it's worth.

But I would say that a good starting point is to figure out what an equivalent hourly rate is, and then discount from there.

There definitely should be a discount given because she is guaranteed business.  I'd say a good discount is 25% off, and as much as 35% to 40% off.  It just kinda depends on the expectations, and whether she can realistically live up to them.

Sounds like you are asking a lot, and she might just be inclined to quote you a rate per time.

Consider her school tuition, books, rent, electric, hydro bill and phone bill.  Decide what percent of this you want to cover.  4-6K would be reasonable without knowing much about her lifestyle.  However, do not commit to year off the cuff.

Often I hear once arrangements of this nature start, young ladies take gents for granted are constantly rescheduling meetings or showing up profoundly late.  

Let her know you want to try it out for a couple of months and if you find things agreeable you'll continue for a year. She has to understand reliability is key or you'll end it.

All the best.