4. A riskfree oneyear bond has a price equal to Fr: 1 and a constant payoff equal to Rr 2 1 . The riskfree 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 (1 point): b. Interpreting the equation above, we can draw conclusions about how real interest rates behave as a function of three different inputs: investors' subjective discomlt factor 6 , the rate of annual consumption growth Cm} CI , 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 riskaverse