Question $8$

Assume zero$-$coupon yields on default$-$free securities are as summarized in the following table:

Maturity $($years$)$

Zero$-$coupon YTM$,$

$1$

$4\mathrm{.}00\%$

$2$

$4\mathrm{.}30\%$

$3$

$4\mathrm{.}50\%$

$4$

$4\mathrm{.}70\%$

$5$

$4\mathrm{.}80\%$

a$.$ What is the price today of a two$-$year, default$-$free security with a face value of $$1000$ and an annual coupon rate of $6\%?$ Does this bond trade at a discount, at par, or at a premium?

b$.$ What is the price of a five$-$year, zero$-$coupon, default$-$free security with a face value of $$1000?$

c$.$ What is the price of a three$-$year, default$-$free security with a face value of $$1000$ and an annual coupon rate of $4\%?$ What is the yield to maturity for this bond?

d$.$ What is the maturity of a default$-$free security with annual coupon payments and a yield to maturity of $4\%?$ Why?

e$.$ Consider a four$-$year, default$-$free security with annual coupon payments and a face value of $$1000$ that is issued at par. What is the coupon rate of this bond?

f$.$ Consider a five$-$year, default$-$free bond with annual coupons of $5\%$ and a face value of $$1000.$

i$.$ Without doing any calculations, determine whether this bond is trading at a

ii$.$ premium or at a discount. Explain. What is the yield to maturity on this bond?

If the yield to maturity on this bond increased to $5\mathrm{.}2\%,$ what would the new price be $?$