The question is in the below

4. A risk-free one-year bond has a price equal to 39; = 1 and a constant payoff equal to Rf 3: 1. The risk-free interest rate is therefore Rf 1. a. Using the fundamental pricing equation, show algebraically that for a representative investor with power utility of consumption with risk aversion parameter 1/ and an annual discount factor of 6, the risk-free interest rate must be equal to the expression below (I point): Rf = l()y 6 ct b. Interpreting the equation above, we can draw conclusions about how real interest rates behave as a mction of three different inputs: investors' Subjective discomt factor 6, the rate of annual consumption growth Ct+1 I ct, and investors' subjective aversion to risk y. Explain the real-world intuition as to why each result listed below should occur. (1 point each) i. When people are impatient, risk-free interest rates are high. ii. Risk-free interest rates are high when annual consumption growth is high. iii. Real interest rates are more sensitive to consumption growth when people are more Iisbaverse c. Find the risk-free interest rate required by a representative investor with a discount factor 6 = 0.9 and a risk aversion parameter 1! = 2. (2 points)