First infer the spot rates from the zero-coupon bonds:

$$r(0,0.5)=-\frac{\ln(97/100)}{0.5}\approx 6.09\%$$ $$r(0,1.0)=-\ln(94/100)\approx 6.19\%$$

The 1.5-year coupon bond has cash flows of $2$at 0.5 years, `$2$ at 1.0 years, and $102`$ at 1.5 years (4.0% annual coupon paid semiannually).

Use the bond price to solve for the 1.5-year spot rate:

$`$95`=2e^{-r(0,0.5)(0.5)}+2e^{-r(0,1.0)(1.0)}+102e^{-r(0,1.5)(1.5)}

Because the first two discount factors come from the zero-coupon prices: $`$95`=2\left(\frac{97}{100}\right)+2\left(\frac{94}{100}\right)+102e^{-1.5r(0,1.5)}

$`$95`=3.82+102e^{-1.5r(0,1.5)}

$`$102`e^{-1.5r(0,1.5)}=91.18 $$r(0,1.5)=-\frac{\ln(91.18/102)}{1.5}\approx 7.49\%$$

Now compute the forward rate from 1.0 to 1.5 years:

$`$0.5`,r(1.0,1.5)=1.5,r(0,1.5)-1.0,r(0,1.0)

$$$$

r(1.0,1.5)=\frac{1.5(7.49%)-6.19%}{0.5}\approx 10.05%

$$Therefore, the correct answer is **C**.$$