Consider a world with two points of time t$0$ and t$1.$ John has just inherited $$5$M $($at t$0).$

He has three projects that he can invest this inheritance in at t$0$:

Project A costs $$1\mathrm{.}0$M at t$0$ and pays off $$1\mathrm{.}700$M at t$1,$

Project B costs $$1\mathrm{.}3$M at t$0$ and pays off $$1\mathrm{.}499$M at t$1$

Project C costs $$2\mathrm{.}0$M at t$0$ and pays off $$2\mathrm{.}180$M at t$1.$

John can also lend and borrow at a bank interest rate of $15$ percent between t$0$ and t$1.($a$)$ Which projects should be undertaken by John? $($b$)$ What is the maximum amount of funds that John could consume tomorrow? $($c$)$ How much more could John consume today over his inheritance if he optimally invests in his real investment opportunities?