A charitable fund is obligated to make payments of $2 million, $3 million, $7 million and $1 million at the end of each of the next four years, respectively. The current zero-rate curve is flat at 9% pa.

1. What is the duration of the fund's obligations? Show your calculations.

D= 2.476

1. The fund wishes to immunise its position using two bonds currently on issue viz bond A which is a 2-year 8% pa bond and bond B which is a 4-year 6% pa bond. Both bonds pay half-yearly coupons and have just paid a coupon. How much should the fund invest today in each bond? Show your calculations.

D₂=1.88

D₄=3.59

1.88w₂+3.59w₄=2.476

w₂=65.43%

w₄=34.57%

2: 65.43%*10.47m

4: 34.57%*10.47m

Please provide detailed handwritten step by step solutions. I need to calculate the answer using hand only. I have the solutions but I want to know how to complete the question. Please do point out if there is any errors.