Assume that you would like to make annual deposits over the next 35 years sufficient to fund a retirement income of $60,000 per year over 30 years of retirement. Assume that you earn a real annual rate of return ?? = 0.07 during your savings years and a real rate of return ?? = 0.04 during your retirement years.

**a.** Find the required level of annual savings ?? = ??.

**2.** Solve the following expression for y where:

**3.** Suppose that we observe the following prices/cash flows for four assets with similar risk:

EOP | A1 | A2 | A3 | A4 |

0 | $95.24 | $98.66 | $109.55 | ?? |

1 | $100.00 | $5.00 | $10.00 | $50.00 |

2 | $0.00 | $105.00 | $10.00 | $50.00 |

3 | $0.00 | $0.00 | $110.00 | $250.00 |

**a.** Use the above information to find the set of effective “discount factors” ?????? (for years t = 1, 2, and 3) implied by the market price data.

**b.** Use the discount factors to recover the implied annual interest rates ???? for years 1, 2, and 3.

**c.** Find the initial “no arbitrage price” for asset A4.

**d.** Suppose that the quoted price for asset A4 was more than your result from part(c). What would this imply?

**e.** (Extra Credit): Assume that the price of asset A4 was $10 less than your answer to part(c). Assume also that you can go long (buy) or go short (sell) any level of these assets in the bond market at time 0. Demonstrate that you can make a risk free profit in this situation.

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