Consider a bond, maturing in $5$ years, with a face value of $1,000,000,$ and a coupon rate of $5\%.$

$1.$ Ifthecurrentlevelofinterestratesis$2\%,$computethepriceofthebondofeachyeartillitmatures. $[$Write down the price formula for each year, before substituting with numbers$].$

$2.$ AssumethatatYear$2,$interestratesincreaseto$10\%.$Whatisthereturnofthebondforaninvestor who bought the bond at Year $1$ and sold it at Year $2?$

$3.$ IfthepriceofthebondatYear$4$isequalto$950,000,$whatistheyield$-$to$-$maturityforthebondat that year?