Final answer:
To calculate the current price, Macaulay duration, and modified convexity of the bond, first adjust the annual coupon rate and annual effective yield rate to their respective monthly values. Then, calculate the current price using the present value formula, and find the Macaulay duration as the weighted average time of all the future cash flows. The modified convexity measures the sensitivity of the bond's price to changes in interest rates. To estimate the price of the bond when the annual effective yield rate is raised to 4.8%, use the modified convexity to adjust the price based on the change in interest rates.
Step-by-step explanation:
To calculate the current price of the bond, we need to calculate the present value of all the future cash flows. Since the bond pays coupon monthly, we need to adjust the annual coupon rate and the annual effective yield rate to their respective monthly values. The monthly coupon rate would be 6% / 12 = 0.5%, and the monthly effective yield rate would be 4% / 12 = 0.3333%.
Using these values, we can calculate the current price using the present value formula. The Macaulay duration can be calculated as the weighted average time of all the future cash flows, and the modified convexity measures the sensitivity of the bond's price to changes in interest rates.
To estimate the price of the bond when the annual effective yield rate is raised to 4.8% using second-order approximation, we can use the modified convexity to adjust the price based on the change in interest rates.