Consider a world with two points in time, t0 and t1. Cynthia Sopwith inherits $2.5 million at t0. She has two projects she can invest this inheritance in at t0. Project A costs $450,000 at t0 and yields $575,000 at t1. Project B costs $950,000 at t0 and yields $1,060,000 at t1. She can also lend and borrow at a bank at an interest rate of 15 percent. Cynthia is only interested in consumption at t1; she does not get any utility from consumption at t0.

(a) Which projects should Cynthia undertake?

(b) What is the most Cynthia can consume at t1? How much does she need to lend or borrow at the bank to achieve this level of consumption?

(c) How would your answers to (a) and (b) be changed if Cynthia could lend to the bank at 10 percent and borrow from the bank at 20 percent?