Jaime will receive with certainty today an endowment of amount $30,000 (y0) and tomorrow an endowment of amount $100,000 (y1). Jaime's preferences are such that, 1) He prefers to consume more than less; and 2) He wants to consume exactly the same amount today and tomorrow. a. If there is no access to capital markets or investment opportunities, what is Jaime's optimal consumption? For questions b. and c., suppose there is a perfect capital market in which Jaime can borrow or lend at the market interest rate of 12%. 

b. Calculate what will be Jaime's maximum future wealth in this capital market. 

c. Calculate the present optimal consumption (C0) of Jaime in this capital market.

 d. If the capital market interest rate changes with a corresponding new optimal consumption of $62,000 today and $62,000 tomorrow, calculate the deficit at t=0 of Jaime's maximum wealth in order to achieve the optimal consumption in the present and in the future (C0, C1) obtained in the previous question, that is, before the change in the capital market interest rate. 

e. Suppose now that Jaime also has the opportunity to invest $25,000 today in a profitable investment project and receive a cash flow tomorrow. Calculate the internal rate of return (IRR) on the project so that Jaime manages to cover the deficit calculated in the previous question.