Based on your photos this looks like brown rot, a fungal disease. This is common on peaches and requires a spray schedule for control.
Many cycles of infection can occur in one growing season and ripening fruits are most vulnerable to infection. A protective fungicide barrier is critical from prebloom through preharvest. It is too late to spray this year.
At least, remove and dispose of fruit mummies from the ground and from trees and always try to remove fruit stems attached to the mummies, if a problem.
Also, be sure to thin the fruits on the tree. A portion of the fruit is removed so that the remainder will develop adequate size. Look at our website for more reasons for thinning the fruit. http://extension.umd.edu/growit/fruit-trees-fruit-thinning
Look at the spray schedule from Va Tech http://extension.umd.edu/growit/home-fruit-preventative-spray-schedule-and-management-common-problem...