A newly issued bond has a maturity of 4 years and pays a 7% coupon rate p.a. (with coupon payments coming once annually). The bond sells at par value with a face value of $1,000.

a) What is the duration of the bond?

b) Find the actual price of the bond assuming that its yield to maturity immediately increases from 7% to 8% (with maturity still 4 years).

c) What price would be predicted by the modified duration rule?

d) explain why the price predicted in (c) does not equal to the actual price in (b).