If you have paid all the interest accrued till today, you owe no interest
as of today. But after one month, you will owe $10K times 0.065/12 or approximately
$54.17 in interest. If you pay that off, then at the end of the next month,
you will again owe $54.17. For the lender, this is "a gift that keeps on giving"
month after month until some day you decide to pay more than the accrued interest and thereby reduce the principal amount owed.
So, now that you have paid off your high interest credit cards (and hopefully
are keeping those balances current, faithfully paying each month's statement
balance in full), and are looking around for investment opportunities,
I would suggest paying down the principal on the student loans first.
You don't have to do it all in one swell foop; you can do it over
months, or years, but get rid of them first.
As Joe Taxpayer said here,
6.5% interest is too high, and it is unlikely that you will make that
kind of money off your investments. Your money is better put to use
paying off those student loans first.