A pension plan is obligated to make disbursements of $$1$ million $($at t$=1),$ $$2$ million $($at $(=2),$ and $$1$ million $($at t$=3)$ at the end of the next three years, respectively. The interest rate $($yield$)$ is $10\%.$Use the above informarion to answer the following questions $29-30\mathrm{.}29.$ What is the duration of the plan's obligations? a$.$ b$.$C$.$d$1\mathrm{.}5625$ years$1\mathrm{.}7624$ years$1\mathrm{.}9524$ years$1\mathrm{.}9967$ years$2\mathrm{.}1033$ years$30.$ The plan wants to fully fund and immunize its position using one$-$year zero$-$coupon bonds and perpetuities, respectively. Assume that yield on these securities is also $10\%.$ How much of its portfolio should be allocated to one$-$year zero$-$coupon bonds to immunize its position?a$\mathrm{.}86\mathrm{.}45\%$b$\mathrm{.}88\mathrm{.}24\%$C$\mathrm{.}90\mathrm{.}48\%$d$\mathrm{.}91\mathrm{.}75\%$e$\mathrm{.}92\mathrm{.}15\%$