Your math is correct, but you have to remember that Google compute instances don't include disk storage or network transfer - you have to pay for those separately, which drives the cost up higher.
It´s even cheaper if you run the vm non-stop. They are offering sustained use discounts.
dfbrown factored that into the calculation (by multiplying by 0.7)
( 0.013 dollars/hour * 24 hours/day * 31 days/month ) * 0.70 discount = 6.77