Answer: d) 6.50%

**Correct answer: D) 6.50%** We first compute the forward rate using the continuously compounded spot rates. ### 1) Forward rate with continuous compounding For the forward period from 1.5 years to 2.0 years: \[ f_{CC}(1.5,2.0) = \frac{R(2.0)\cdot 2.0 - R(1.5)\cdot 1.5}{2.0-1.5} \] Substitute the values: \[ f_{CC}(1.5,2.0) = \frac{0.046\cdot 2.0 - 0.040\cdot 1.5}{0.5} = \frac{0.092 - 0.060}{0.5} = 0.064 \] So the 6-month forward rate is **6.4% continuous compounding**. ### 2) Convert to semi-annual compounding Let the semi-annual-compounded annual rate be \( r_{SA} \). Over 6 months, the accumulation must match: \[ 1 + \frac{r_{SA}}{2} = e^{0.064\cdot 0.5} = e^{0.032} \] \[ 1 + \frac{r_{SA}}{2} \approx 1.03252 \] \[ \frac{r_{SA}}{2} \approx 0.03252 \quad\Rightarrow\quad r_{SA} \approx 0.06504 = 6.50\% \] ### Final answer The nearest choice is **6.50%**.

Author: Manit Arora