Michael has a $$1$M endowment. He can borrow or lend from a bank at $20\%.$ He allocates wealth between youth and old age. What should he do$?1.$ He can go on a trip around the world $,$ and then live in poverty when he's older $.2.$ He can go on a smaller trip $,$ have a moderate lifestyle in his youth $($ spending $ $0\mathrm{.}5$M $),$ and still have $0\mathrm{.}5(1\mathrm{.}2)=\backslash$$$0\mathrm{.}6$M for when he's old $3.$ He can put all of his money in a bank and go on an even better trip when he's older $($$$1\mathrm{.}2$M $).$