a) A pension plan is obligated to make disbursements of $1 million, $2 million, $5 million and $1 million at the end of each of the next four years, respectively. Find the duration of the plans obligations if interest rates are flat at 10% annually.

b) If the plan in the previous question wants to fully fund and immunise its position, how much of its portfolio should it allocate to one-year zero-coupon bonds and perpetuities, respectively, if these are the only two assets funding the plan?