Calculating the duration of a 9% coupon, 8% yield to maturity, 4-year annual payment bond, if the coupon rate decrease and other factors remain the same, the duration for new bond will ? A. 4.1004 years; increase B. 3.5396 years; increase C. 2.2989 years; decrease D. 4.0000 years, increase

First, let's calculate the duration of the original bond:

1. Determine the cash flows: For a 4-year bond with a 9% coupon rate, the annual cash flows are $9 (9$100 par value) for each of the first three years, and $109 ($9 coupon payment + $100 principal repayment) in the fourth year.

2. Assign weights to each cash flow: The present value of each cash flow is calculated by discounting it using the 8% yield to maturity. The present values are approximately $8.33,$7.71, $7.14, and$79.38, respectively.

3. Calculate the weighted average time to receive each cash flow: Multiply the present value of each cash flow by the time until it is received (in years). The results are approximately $8.33,$15.42, $21.42, and$317.52, respectively.

4. Divide the sum of the weighted average time to receive each cash flow by the bond's current market price: The sum of the weighted average times is $362.69. The current market price of the bond is the sum of the present values of the cash flows, which is$102.56. Therefore, the duration of the bond is $362.69 /$102.56 = 3.5396 years.

Now, let's consider the effect of a decrease in the coupon rate. If the coupon rate decreases and all other factors remain the same, the bond's cash flows will decrease. This will increase the weight of the final principal repayment in the calculation of duration, which will increase the duration of the bond.

Therefore, the answer is:

B. 3.5396 years; increase