Problem for Wednesday evening $($December $13$th$,2023)$Suppose that an investor has an eight$-$year investment horizon $(16$ semesters$).$ The investor is considering a $14-$year $8\%$ coupon bond selling at par $($$ $1000).$ The investors expectations are as follows:$1.$ The first six $(6)$ semiannual coupon payments can be reinvested from the time of receipt to the end of the investment horizon at a simple annual interest rate of $7\%\mathrm{.}2.$ The last tent $(10)$ semiannual coupon payments can be reinvested from the time of receipt to the end of the investment horizon at a $9\%$ simple annual interest rate$\mathrm{.}3.$ The required yield to maturity on six$-$year bonds at the end of the investment horizon will be $12\mathrm{.}9$

"Answer like the example"

Suppose that an investor has a six$-$year investment horizon $(12$ semesters$).$ The investor is

considering a $13-$year $9\%$ coupon bond selling at par $($$$1000).$ The investor's expectations are as follows:

The first four $(4)$ semiannual coupon payments can be reinvested from the time of receipt to the end of the investment horizon at a simple annual interest rate of $8\%.$

The last eight $(8)$ semiannual coupon payments can be reinvested from the time of receipt to the end of the investment horizon at a $10\%$ simple annual interest rate.

The required yield to maturity on seven$-$year bonds at the end of the investment horizon will be $10\mathrm{.}6\%.$

Coupon $=C=9\%**\frac{1000}{2}=$$$45$

Step $1$: Coupon payments of $$45$ every six months for six years $($the investment

Talking $5$ :

horizon$)$ will be received. The coupon interest plus interest on interest for the first four coupon payments, assuming a semiannual reinvestment rate of $4\%,$ is

coupon interest

$=$$$45[\frac{(1\mathrm{.}04{)}^4-1}{0\mathrm{.}04}]$

interest $on$ interest

$=$$$191\mathrm{.}09$

This gives the coupon plus interest on interest as of the end of the second year $($four periods$).$ Reinvested at $4\%$ until the end of the planned investment horizon, four years or eight periods later, $$191\mathrm{.}09$ will grow to

$$191\mathrm{.}09(1\mathrm{.}04{)}^8=$$$261\mathrm{.}52$

The coupon interest plus interest on interest for the last eight coupon payments, assuming a semiannual reinvestment rate of $5\%,$ is