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The time-weighted compounded

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You purchase a stock for $100 that pays an annual dividend of $5.50. At the beginning of the second year, you purchase an additional share for $130. At the end of the second year, you sell both shares for $140. Determine the dollar-weighted return and the time-weighted compounded (i.e., geometric) return on this investment. Repeat the process but assume that the second share was purchased for $110 instead of $130. Why do the rates of return differ?

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