i$)$ Find the price of a two$-$year bond with face value of $$100,$ six monthly coupons of $8\%$ per

annum and yield of $6\%$ per annum, where it is purchased with $60$ days to the first coupon

payment and there are $181$ days in the coupon period.

ii$)$ Given a four$-$year bond with face value of $$10,000,8\%$ annual coupon and yield of $6\%$ per

annum, use the duration measure to estimate the change expected in the bond price if the yield

increases to $7\%.$

iii$)$ An insurance company must make payments to a customer of $$2$ million in two years and $$4$

million in three years. Bonds currently yield $10\%$ per annum.

a$)$ What is the present value and duration of the company's obligation?

b$)$ To immunise its obligation, what must be the maturity and face value of a zero$-$coupon

bond?