a$)$ Bond A has three years to maturity, with an annual coupon rate of $4\%.$ Its yield to maturity is $3\%.$ Consider a face value of $$100.$ Compute the price of bond A$.(3$ marks$)$

b$)$ Bond B has three years to maturity, with an annual coupon rate of $3\%.$ Consider a face value of $$100.$ The one, two$-$ and three$-$year spot interest rates are $1\%,2\%$ and $3\%,$ respectively. Compute the price of bond B$.(3$ marks$)$

c$)$ Give a brief overview of the relationship between interest rates and bond prices. Use a graph for your answer. $(5$ marks$)$

d$)$ Consider the following information for bond C: it pays annual coupons with a coupon rate of $6\%,$ it has two years to maturity, the one$-$year spot rate is $2\mathrm{.}5\%$ and the bond's yield to maturity Is $5\mathrm{.}2\%.$ What is the two$-$year spot rate? Consider a face value of $$100.(9$ marks$)$