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

$1.$ If the current level of interest rates is $2\%,$ compute the price of the bond of each year till it matures.

$[$Write down the price formula for each year, before substituting with numbers$].$

$2.$ Assume that at Year $2,$ interest rates increase to $10\%.$ What is the return of the bond for an investor

who bought the bond at Year $1$ and sold it at Year $2?$

$3.$ If the price of the bond at Year $4$ is equal to $950,000,$ what is the yield$-$to$-$maturity for the bond at

that year?