Consider the 4 bond, with maturity 30 months, and maturity value $100,000, trading at $99,468.75. (The yield to maturity on the bond is y = 0.023012 in semi-annual rate.) Assume a flat spot curve. (a) Calculate the price value of modified duration, Macaulay duration, and convexity. (b) Assume interest rates suddenly increase by 100 basis points. Calculate the actual change in the bond's price. (c) Compare the actual price change with the approximated price change using duration alone, and using both duration and convexity.