Answer: 10.05%

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: $$ 95=2\left(\frac{97}{100}\right)+2\left(\frac{94}{100}\right)+102e^{-1.5r(0,1.5)} $$ $$ 95=3.82+102e^{-1.5r(0,1.5)} $$ $$ 102e^{-1.5r(0,1.5)}=91.18 $$ $$ r(0,1.5)=-\frac{\ln(91.18/102)}{1.5}\approx 7.49\% $$ 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**.

Author: Manit Arora