$.$ Consider the following $$1,000$ par value zero$-$coupon bonds:

Bond Year to Maturity Yield to Maturity A $15\%$

B $26\%$

C $36\mathrm{.}5\%$

D $47\%$

You take the expectations hypothesis to estimate the forward rate. What is the market$$s expectation of the yield curve one year from now? Specifically, what are the expected values of next year$$s yields on bonds with maturities of $($a$)1$ year; $($b$)2$ years; $($c$)3$ years?

$2.$ A newly issued bond pays its coupons once a year. Its coupon rate is $5\%,$ its maturity is $20$ years, and its yield to maturity is $8\%.$ Find the holding$-$period return for a one$-$year investment period if the bond is selling at a yield to maturity of $7\%$ by the end of the year. Find the realized compound yield for a two$-$year holding period, assuming that $($i$)$ you sell the bond after two years, $($ii$)$ the bond yield is $7\%$ at the end of the second year, and $($iii$)$ the coupon can be reinvested for one year at a $3\%$ interest rate.

$3.$ Bonds of Carthage Corporation with a par value of $$1,000$ sell for $$960,$ mature in five years, and have a $7\%$ annual coupon rate paid semiannually. Calculate $($a$)$ Current yield, $($b$)$ Yield to maturity, and $($c$)$ Horizon yield $($also called realized compound return$)$ for an investor with a three$-$year holding period and a reinvestment rate of $6\%$ over the period. At the end of three years, the $7\%$ coupon bonds with two years remaining will be sold at yield to maturity of $7\%.$