Dementia, Alzheimer's disease in particular, is one of the major causes of disability and decreased quality of life among the elderly and a leading obstacle to successful aging. Given the profound impact on public health, much research has focused on the age-specific risk of developing dementia and the impact on survival. Early work has discussed various methods of estimating age-specific incidence of dementia, among which the illness-death model is popular for modeling disease progression. In this article we use multiple imputation to fit multi-state models for survival data with interval censoring and left truncation. This approach allows semi-Markov models in which survival after dementia depends on onset age. Such models can be used to estimate the cumulative risk of developing dementia in the presence of the competing risk of dementia-free death. Simulations are carried out to examine the performance of the proposed method. Data from the Honolulu Asia Aging Study are analyzed to estimate the age-specific and cumulative risks of dementia and to examine the effect of major risk factors on dementia onset and death.