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 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 in (c) does not equal the actual price in (b)