A three$-$year bond has a coupon rate of $5\%$ and is priced at $$973\mathrm{.}27.$ The face value is $$1,000$ and the bond pays annual coupons.

a$)$ Calculate the realized $($annualized$)$ compound YM on the bond if the one$-$year interest rate $($with

certainty$)$ over the next three years will be$,$ ri $=5\%,$ r$2=6\%,$ and rs$=8\%.$ You buy the bond today and

hold it until maturity.

Note: Assuming today is t $=0$ and t $=1$ is one year from today, ri represents the interest rate for the period

t$=0$ to t $=1.$ Similarly, rz represents the interest rate for the period t $=1$ to t $=2,$ and ra represents the

interest rate for the period t $=2$ to t $=3.$

b$)$ Calculate the realized $($annualized$)$ compound retur for an investor with a two$-$vear holding period. The

investor buys the bond today and sells it at the end of two years $($i$.$e$.,$ at t $=2)$ after receiving the coupon

payment. Use the interest$-$rate data from part A