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This paper proves a Berry-Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be O(n-1/2) as n -> infinity, where n denotes the sample size. This result is in sharp contrast to the case of the sample mean of strongly-mixing random variables where the rate O(n-1/2) is not known even under an exponential strong mixing rate. The main result of the paper has applications in finance and econometrics as financial time series important data often are heavy-tailed and quantile based methods play an role in various problems in finance, including hedging and risk management.