Final answer:
To calculate the current price of the bond, use the present value formula. Calculate the Macaulay duration by finding the present value of each cash flow and multiplying it by the time it is received.
Step-by-step explanation:
To calculate the current price of the bond, we can use the present value formula. The bond pays an annual coupon of 6%. Let's assume the face value is $1000. The bond pays coupon monthly, so the monthly coupon payment is (0.06/12) * 1000 = $5. The bond has a 10-year maturity, so the total number of coupon payments is 10 * 12 = 120. The current price of the bond can be calculated as the present value of all the future cash flows (coupon payments and face value). Using a discount rate of 4%, we can use the present value formula to find the current price. The formula is: Current Price = (Coupon Payment / Discount Rate) * (1 - (1 + Discount Rate)^-n) + (Face Value / (1 + Discount Rate)^n) where n is the number of periods. Plugging in the values, we get: Current Price = (5 / 0.04) * (1 - (1 + 0.04)^-120) + (1000 / (1 + 0.04)^120) = $936.09.
To calculate the Macaulay duration of the bond, we need to find the present value of each cash flow and multiply it by the time it is received. The Macaulay duration is the weighted average time until the cash flows are received. We can use the same discount rate of 4% to find the present value of each cash flow and multiply it by the corresponding time period. Summing these values gives us the Macaulay duration. Modified convexity is a measure of the sensitivity of the bond's price to changes in interest rates. It can be calculated using the formula: Modified Convexity = (1 / Current Price) * (Sum of (Present Value * Time Period^2)). Using the same discount rate of 4%, we can find the present value of each cash flow and calculate the modified convexity using the formula. Estimate the price of the bond when the annual effective yield rate is raised to 4.8% using second-order approximation.