First to actually answer the question "how long at these rates/payments?"-
- $6153 3%, $36/mo = 223 months remain
- $5200 2.5%, $30/mo = 215 months remain
- $940 8.75%, $9/mo = 197 months remain
These is nothing magic or nefarious about what the bank is doing. They add accrued interest and take your payment off the new total.
I'd make higher payments to the 8.75% debt until it's gone, $100/mo extra and be done. The first debt, if you bump it to $50 will be paid in 147 months, at $75/mo, 92 months. Everything you pay above the minimum goes right to the principal balance and gets you closer to paying it off.
The debt snowball is not the ideal way to pay off your debt. Say I have one 24% credit card the bank was nice enough to give me a $20,000 line of credit on. I also have 20 cards each with $1000 in credit, all at 6%. The snowball dictates that the smallest debt be paid first, so while I pay the minimum on the 24% card, the 6% cards get paid off one by one, but I'm supposed to feel good about the process, as I reduce the number of cards every few months.
The correct way to line up debt is to pay off the (tax adjusted) highest rate first, as an extra $100 to the 24% card saves you $2/mo vs 50 cents/mo for the 6% cards. I wrote an article discussing the Debt Snowball which links to a calculator where you can see the difference in methods. I note that if the difference from lowest to highest rate is small, the Snowball method will only cost you a small amount more. If, by coincidence, the balances are close, the difference will also be small.
The above aside, it's the rest of your situation that will tell you the right path for you. For example, a matched 401(k) deposit should take priority over most debt repayment. The $11,000 might be better conserved for a house downpayment as that $66/mo is student loan and won't count as the housing debt, rather "other debt" and part of the higher ratio when qualifying for the mortgage. If you already have taken this into account, by all means, pay off the 8.75% debt asap, then start paying off the 3% faster. Keep in mind, this is likely the lowest rate debt one can have and once paid off, you can't withdraw it again. So it's important to consider the big picture first.
(Are you depositing to a retirement account? Is it a 401(k) and are you getting any matching from the company?)