Question 4 a) Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity

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Question 4
a) Find the duration of a 6% coupon bond making annual
coupon payments if it has three years until maturity and has a
yield to maturity of 6%. Note: The face value of the bond is
£1,000.
[5 marks]
b) What is the duration if the yield to maturity is 10%?
Note: The face value of the
bond is £1,000.
[5 marks]
c) An insurance company must make payments to a customer
of £10 million in one year and £4 million in five years. The yield
curve is flat at 10%. If it wants to fully fund and immunize its
obligation to this customer with a single issue of a zero- coupon
bond, what maturity bond must it purchase?
[5 marks]
[Total of Question 4: 15 marks]