3. Consider $1000 face value of a zero-coupon bond with 20 years to maturity.

(a) What is the Macaulay duration of this bond?

(b) What is the modified duration of this bond if the price today is $372.43?

(c) Suppose the bond is yielding 6.2% and this changes to 6.3%. What percentage price change is predicted by the (modified) duration at the 6.2% yield? What actual percentage price change occurs? Answer with at least four decimal places.