An investor with a $8-$year horizon purchases a bond with a par value of $$1000,20$ years

to maturity, and a $5\%$ coupon rate. Bonds with similar risk characteristics and the same

maturity are presently yielding $7\%.$

a$)$ Find the price of the bond?

b$)$ The investor believes that he will be able to earn $6\%$ annually on the reinvested

coupons. Identify the coupon interest and the interest on interest from holding

the bond for $8$ years.

c$)$ The investor believes that in $8$ years, this bond$$s yield to maturity will be $6\%.$

Find the price of the bond in $8$ years if the investor is correct in his interest rate

projection.

d$)$ If the investor$$s assumptions are correct and he sells the bond in $8$ years,

calculate his annual return from this investment.