A pension plan is obligated to make disbursements of $$1$ million, $$2$ million, and $$1$ million at the end of each of the next three years, respectively. Find the duration of the plan's obligations if the interest rate is $10\%$ annually. $($LO $11-2)$

If the plan in the previous problem 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? $($LO $11-4)$