That sounds like a pretty good price, actually.
Private lessons that I've hunted for start at $35 for a half hour (if I'm lucky) and go up from there. When I was taking private saxophone lessons about 10 years ago, it was still about $25-$30 for a half hour.
Though, I'm sure you could hunt around and find it for less somewhere. You could possibly even barter with a teacher. When I was younger and taking voice lessons, my teacher gave them to me for only $10 for a half hour and I would also walk her dog.
My current dance teacher will trade lessons for doing some painting around her house, or gardening, or sewing.
Unfortunately, private lessons are pricey – it's just the nature of the beast. But, like I said, you can find better deals if you really search – or you could always find a group lesson.