$1.$Suppose a$$ five$-$year, $ $1000$ bond with annual coupons has a price of $ $898\mathrm{.}64$ and a yield to maturity of $5\mathrm{.}5\%.$ What is the$$ bond's coupon$$ rate?

$2.)$ The yield to maturity of a $ $1000$ bond with a $6\mathrm{.}8\%$ coupon$$ rate, semi$-$annual$$ coupons, and two years to maturity is $7\mathrm{.}8\%$APR$,$ compounded$$ semi$-$annually. What must its price$$ be$?$

$3.)$ Assume that a bond will make payments every six months as shown on the following timeline$($using six$-$month$$ periods$)$:

The timeline starts at Period $0$ and ends at Period $30.$ The timeline shows a cash flow of $ $19\mathrm{.}01$ each from Period $1$ to Period $29.$ In Period $30,$ the cash flow is $ $19\mathrm{.}01$ plus $ $1,000.$

Period $1,2,29,30$

Cash Flows: $ $19\mathrm{.}01,$$$19\mathrm{.}01,$$$19\mathrm{.}01,$$$19\mathrm{.}01+$$ $1,000$

a$.$ What is the maturity of the bond$($in years$)?$

b$.$ What is the coupon rate$($as a$$ percentage$)?$

c$.$ What is the face$$ value?