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请教一道关于value of future contract, with dividend

大家好, level 1 有道例题:


The price a 6-month forward contract for which the underlying asset is a stock index with a value of 1,000 and a continuous dividend yield of 1%. Compute the value of a long position of the index increase to 1,050 immediately after the contract is purchase.
答案给的是:
1,050e^(-0.01*(0.5)) -1,015e^(-0.04*(0.5) )=49.75

我不理解的是,为什么第一个price只要compound dividends, 而不用compound Risk free rate

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