This paper studies the formation and anchoring of long-run inflation expectations under bounded rationality and adaptive learning. The empirical analysis applies this framework to India, which provides a useful setting given its recent transition to a formal inflation-targeting regime. Motivated by the persistence of elevated termpremia in India’s sovereign bond market, we develop and estimate a New Keynesian model in which agents update beliefs about long-run inflation in response to short-horizon forecast errors, implying that expectations may remain imperfectly anchored even under an explicit inflationtargeting regime. The model is estimated using inflation data and survey-based short-run inflation expectations from India, allowing us to recover quarterly movements in ten-year-ahead inflation expectations. We find that the introduction of inflation targeting lowered the level of long-run inflation expectations and moved them closer to the policy target. However, long-run beliefs remain sensitive to short-run inflation surprises, consistent with adaptive learning and incomplete anchoring. This persistent belief updating generates long-horizon inflation uncertainty, which is priced into nominal bond yields and contributes to elevated termpremia at longer maturities. Counterfactual simulations show that fully anchored expectations would substantially reduce long-horizon inflation uncertainty and lower long-maturity term premia by around 120 basis points. The results highlight how bounded rationality in expectation formation can sustain inflation risk and termpremia despite improvements in monetary policy credibility.