Question 2.33: How long will it take for the price of the coupon bond in Ex...

In Figure S.2 we can see that the bond price will reach $95 for the first time during year one, when the bond price is given by 10e^{r(t−1)}+10e^{r(t−2)}+10e^{r(t−3)}+ 10e^{r(t−4)} + 110e^{r(t−5)}. Putting r = 0.12, we can find the desired time t when the price will reach $95 by solving the equation

10e^{r(t−1)} + 10e^{r(t−2)} + 10e^{r(t−3)} + 10e^{r(t−4)} + 110e^{r(t−5)}=95.

This gives t ≅ 0.4257 years or 155.4 days.