1. A pension plan is obligated to make disbursements of $3.5 million, $4.0 million, $4.5 million, and $5.0 million at the end of each of the next four years, respectively. Find the duration of the plan’s obligations if the interest rate is 7% annually.
2. If the plan from the question above wants to fully fund and immunize 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?
Please show work and write out answers.