For those of you who haven't heard, Google has gotten into the Mobile network game with its Project Fi. I signed up for early adoption a few weeks ago and a little after receiving my invite, decided to switch over from Sprint.

Just a picture of Fi
I am a budget conscious college student. I subsist on mainly coffee and lab work, so financially justifying the swap to Fi was important. Fi runs at pretty low rates, but to fully swap over, I would need to get a new and rather pricey, phone; the Nexus 6. Despite, getting a new phone- Fi made sense. Here's the math (for me at least)

$$ fi(n) = $532 + n\cdot\left($20 + $10\cdot\left[\frac{gigs}{2} \pm \frac{gigs}{2}\right]\right)$$
$$ sprint(n) = n\cdot\left($90 \pm spread\right)$$

$$ n\in\mathbb{N} $$

So for this to work, I need a reasonable time frame on $fi(month) \le sprint(month)$. Best case I've made my money back on the phone in 8 months, worst case I make in back in 13. It's important to note that this is referring to strictly liquid asset savings. If we account for the value of the phone, Fi is the better choice by far. It's worth the investment. Here's a simple graph and calculator for your own use:

Average payment now: Cost Spread: Gigs per month: Cost on Nexus:

Best Case Timeline
Worst Case Timeline

Overall the service works beautifully, the Nexus 6 is gorgeous and I am happy.

My initial reaction was to model the services as 2 distinct Markov chains where I included the probability of breaking a phone, but this seemed like to much effort considering I already made the swap. I have a tendency to over complicate things