A stooped posture is a common postural problem in older people. In the medical field, this posture is called kyphosis of the thoracic spine (mid back). Kyphosis is defined as excessive rounding of the mid back and is associated with increased compression fractures of the spine and decreased balance.
Research has shown that people that do more extension based exercises at a young age will continue to reap the benefits of this type of exercise as they get older even if they stop doing extension based exercises. The improvements seen with extension based exercises are increased back strength (Sinaki 1984, Sinaki 2005), decreased compression fractures (Sinaki 1984, Sinaki 2005) and improved posture (Sinaki 2005, Katzman, 2010).
Lying on your stomach (prone position) and lifting the head and chest will work on increasing back strength. Adding arms and legs lifting will further challenge the spinal muscles. Mix things up and hold the position for 5-10 seconds to work endurance or dynamically alternate the movements of the arms and legs.
The exercise below is called Swimmer and is done with the Hooked on Pilates HANDIBANDs. Draw your stomach and buttocks tight to help support the low back, lift the head and chest slightly and maintain this position as the arm and opposite leg lifts, alternating from side to side. Do 50-100 repetitions on each side.