You are the portfolio manager of a large company that invests in many securities including corporate bonds. You have been assigned the task of bond portfolio management. You are provided with the following data in relation to bonds: Maturity period 7 years Coupon rate 12% Par value $1,000 Coupons on bonds are paid annually Yield to maturity of bonds 8% Required: i) Calculate the Macualay's duration, modified duration and convexity ii) Calculate the change in bond price when yield to maturity changes by one percent using modified duration iii) Calculate the change in bond price when yield to maturity changes by one percent when convexity is considered.

Please provide with calculations.