# Question: 1 suppose i offered you the following bond the bond...

###### Question details

1. Suppose I offered you the following Bond. The bond pays out $200 per year for ten years, then pays the principal payment $5000 at the end of the contract period. If I offered you this bond for $3,156.63 What is the rate of return on this bond?

2. There are two investment projects: one risky, paying $200 with probability 0.40 or $150 with probability 0.60, or a riskless project paying $160. Further, suppose Rosa's utility function can be approximated by 𝑈(𝑥) = √𝑋 where X denotes the payoffs she receives. What project should she choose? What is the expected value on the risky project? Calculate the Risk-Premium of the risky investment.

3. Suppose you are renting a home in a rough part of town. You are considering purchasing rental insurance to cover losses associated with a burglary. Your initial wealth is 10,000. You believe that the probability of a break-in is 0.10 and this would result in a wealth loss of 8,000. If there is no breakin, then your wealth remains the same. Suppose your utility function for any level of wealth x equals u(x) = ln(x).

a) What is the actuarially fair insurance rate?

b) If the insurance company charges you the actuarially fair insurance rate, show that this risk averse individual will accept and pay for full-coverage rental insurance.

PLease show all steps including formulas, thank you.