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.

a) What is the duration of the funds obligations? Show your calculations.

b) 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.

c) Assuming the fund can buy bonds with any desired par value, what is the required par value for bond A and what is the required par value of bond B? Show your calculations.