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Arithmetic processing is represented in a fronto-parietal network of the brain. However, activation within this network is thought to undergo a developmental shift from domain-general cognitive processing in the frontal cortex towards domain-specific magnitude processing in the parietal cortex. This assumption is primarily based on findings in children and young adults. In this registered report, we set out to replicate the proposed gradual fronto-parietal activation shift in arithmetic processing and, for the first time, to explore how neural development of arithmetic continues during aging. This registered report focuses on the behavioral and neural correlates of arithmetic and arithmetic complexity across the lifespan, i.e., childhood, when arithmetic is first learned; young adulthood, when arithmetic skills are well established already, and old age, when individuals have lifelong arithmetic experience. Therefore, brain activation during mental arithmetic was measured in children, younger adults, and older adults using functional near-infrared spectroscopy (fNIRS). Arithmetic complexity was manipulated via carry and borrow operations in two-digit addition and subtraction. The results provide evidence that increasing arithmetic complexity is associated with increased activation in the fronto-parietal network across all age groups. Even though behavioral carry and borrow effects decrease during development, suggesting improvements in place-value processing, the underlying categorical and continuous processing characteristics and cortical activation remain relatively stable. While frontal activation may decrease from childhood to adulthood, parietal activation does not show a corresponding increase. Thus, the developmental fronto-parietal shift in arithmetic processing might only apply to single-digit arithmetic - but not to two-digit arithmetic across the lifespan. Overall, these results suggest that arithmetic skills acquired in childhood are maintained throughout the lifespan.