Answer: 0.1398

## Explanation To convert a simple return to a continuously compounded return, we use the relationship: $$1 + R_t = e^{r_t}$$ Where: - $R_t$ = simple return (15% or 0.15) - $r_t$ = continuously compounded return Solving for $r_t$: $$r_t = \ln(1 + R_t) = \ln(1.15)$$ Calculating this: $$r_t = \ln(1.15) = 0.1398 = 13.98\%$$ Therefore, the equivalent continuously compounded return is **0.1398** or **13.98%**. This conversion is important in quantitative finance because continuously compounded returns have several advantages: - They are additive over time - They are normally distributed in many financial models - They are used in options pricing models like Black-Scholes

Author: Tanishq Prabhu