You could also contact the state Children's Welfare Department (or whatever it is called in your state--our state has changed the name like 3 times in recent years....) They have guidelines for the age that it is OK for children to stay home alone.
I personally believe that 13 is OK. I was babysitting other people's children at age 12. I have had a few 13-year olds babysit for me.....
Of course, if it were longer than an hour or two, I would have greater concern.
In answer to the cost of nannys. My sister is a nanny with about 3 years experience, and she was getting $400/week. (Not sure what her hours were--I think it was full-time for one child, a few hours/day for two other children.)