A 1-year zero coupon bond with face value $100 sells for $96.70, a 2-year zero coupon bond sells for $91.20, a 3-year zero coupon bond sells for $85.00, and a 4-year zero coupon bond sells for $80.00. (SHOW ALL WORK INCLUDING FORMULAS)

Calculate the modified duration of the 4-yr zero

What is the predicted dollar price change of the 4-year zero coupon bond using the duration approximation, assuming that the yield to maturity across all horizons increases by 1%?

How does it compare with the actual change in price?