T-Mobile's New G2 and Why You Should Know Math / Finance

I was looking for my wife a new cell phone, and ran across a math / finance problem.  Look at this screen shot:

For a math professor, like Dan Myer, it has all the information that is needed.  It poses questions, many of them:

• Which plan is cheapest?
• When does the 500 minutes plan become more expensive than the 1000 minutes plan?
• Should I purchase the phone for $499 or $199 given the change to the plan values?
• Is there another carrier who is cheaper?
• . . .

The question I am going to deal with is, "Should I purchase the phone for $499 or $199 given the change in the in the plan values?"  For this experiment, I am going to use the Unlimited Minutes to test.

$499 + 79.99 * 24 is less than $199 + 99.99 * 24.  Therefore, I should purchase the phone outright on a math basis.

Given you could invest the difference at 2%, the differing NPV's are about $170 difference.  You're cost of capital for the contract is about 9% between the two plans.  The cost of capital is a differential IRR equation.  $-300 now, but $20 more per month over the next 24 months, which equates to 9%.

This figuring doesn't include the taxes and fees, which would presumably be higher on the $99.99 / month plan than the $79.99 / month plan.  Giving even more lee-way to purchasing the phone in the beginning.