A US government bond maturing in $2$ years has a fixed coupon rate of $2\mathrm{.}5\%$ pa$,$ paid semi$-$annually.

The bond's yield$-$to$-$maturity $($YTM$)$ is currently $4\mathrm{.}5\%$ pa$,$ given as an annualised percentage rate $($APR$)$ compounding semi$-$annually.

The face value of the bond is $$100.$ Calculate the bond price. All answer options below are rounded to $6$ decimal points.

Question $2$ Select one:

a$.$

$$96\mathrm{.}21526$

b$.$

$$103\mathrm{.}878058$

c$.$

$$105$

d$.$

$$105\mathrm{.}0625$

e$.$

$$109\mathrm{.}2025$