(1) An employee must decide how to invest his retirement savings 10. He is offered only two options: a xed interest rate bond or a mutual fund invested in the stock market. The bond returns a xed interest rate r3 = 0.1. The mutual fund growth rate 1'}: is random: with probability 1 / 2 the rate is low: n: = 0.1 and with probability 1/2 the rate is high: 7'}: = 0.4. Thus, if the employee invests yin the mutual fund, he gets paid 0.93; if 7'}; = 0.1 and 1.4g if n: = 0.4. The employee has utility function u(z) = log(z) for nal wealth z. (a) If the employee invests a: in the bond and w a: in the mutual fund, what is the nal wealth of the employee when the mutual fund growth rate is low and when it is high? (b) Optimally, how much of his savings should the employee invest in the bond and how much should he invest in the mutual fund