Continuously compounded returns for an asset that increases in price from S1 to S2 over time period t (assuming no dividends or other distributions) are given by:
Choice 'd' is the correct answer. Continuously compounded returns are given by the log of S2/S1. The expression (S2 - S1)/S1 gives discrete returns, not continuously compounded returns.
Note that the question is only asking for the return over the given time period, not annualized returns. So t is not relevant here. If we had to find annualized returns, and t were expressed in years, then the annualized return would have been (1/t)*ln(S2/S1).
Also refer to the tutorial on interest rates and compounding for more information on continuously compounded rates.
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