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%.