Use the following information for problems 1, 2, 3, and 4: A non-callable $1,000 par- value bond matures in thirty years at par. The annual coupon rate is 5% with coupons payable annually. The bond was purchased at a price to yield an annual effective rate of 4%. 1. (1 point) Find the bond purchase price. 2. (1 point) Calculate the Macaulay duration and the modified duration for this bond. 3. (2 points) Suppose that the market interest rate increases to 4.5%. Calculate the price of the bond at 4.5% using the first-order Macaulay approximation, 4. (2 points) Suppose that the market interest rate increases to 4.5%. Calculate the price of the bond at 4.5% using the first-order modified approximation