I understand your math, maybe because i've crunched them too.
With 8 yrs to go, minimum payments.
Yr 1
$833 x 12 = ~$10k
Yr 2
$900 x 12 = $10,800
Yrs 3-8
$1000 x 72 = $72,000
Total = ~$93k (close to your $96,466) total amount of debt paid
With
Yr 1
$50k invested
Yrs 2 & 3
$10k/yr invested
Total = $70k (+ 7% compounding over 8 yrs)
Total investments = $117k
OR
Yr 1
$10k min payments + $50k = $60k
Yr 2 & 3
$10k/yr min ($20k) + $10k/yr extra ($20k) = $40k
Total = ~$100k (loans paid off)
Yrs 4-8
$12k/yr (which was the min payment, now invested) =$60k (+ compounding of 7% over 5 yrs)
Total investments=~$69k
Hope that helps clarify to others...
Yes, i think your math is correct...theorectically, yes you will "make" $48k MORE by investing your money rather than paying off your debt. The biggest issue is that shit happens, and a lot of shit can happen in 8yrs.
I'd go a step further, to get the most benefit. You want these minimum payments to be as small as possible. The way to do that is to lower your AGI. The easiest way to go all traditional, no more Roth, and to max those out. I understand the years almost over and your wife may not be able to max it out, but she should contribute as much as possible for 2014 and then for the next 8 yrs max them out. Also, even though you've already maxed out your Roth ira for 2014, you can call and have them "recharacherized" for 2014, and max out your wifes traditional IRA for 2014.
Here's some math so you can see what i'm saying. Assumes your agi for 2014, after maxing your tsp, is the same. (I know i don't have all your exact info)
$97k AGI
-$17,500 (wifes 401k)
-$11,000 (traditional IRA x 2)
= $68,500 (new, lower AGI)
Which means new lower minimum payment on IBR = $560/month x 8 yrs = ~$55k (total paid)
https://studentloans.gov/myDirectLoan/mobile/repayment/repaymentEstimator.action#view-repayment-plansAlso, having kids lowers your minimum payment...not saying you should have them, just an fyi...