Step 1: The question asks which hormone shows a rising level as a person gets older. Among the options, parathyroid hormone (PTH, parathormone) is the one that classically increases with advancing age.
Step 2: With ageing there is reduced renal hydroxylation of vitamin D, lower calcium absorption from the gut, and a tendency to mild hypocalcaemia. The parathyroid glands respond by secreting more PTH, a state often called secondary or senile hyperparathyroidism.
Step 3: The chronically raised PTH increases bone resorption to maintain serum calcium, and this is one contributor to age-related bone loss and osteoporosis.
Step 4: Why the others are wrong: growth hormone (GH) declines steadily after young adulthood (somatopause), prolactin does not rise as a normal ageing feature, and insulin secretion and sensitivity generally fall with age. So the correct answer is parathormone.