## Yieldto Maturity

3.1 On May 15, 2001, the price of the 11.625s of November 15, 2002, was 110-214/4. Verify that the yield-to-maturity was 4.2139%. Explain this yield relative to the spot rates from question 2.3.

3.2 On May 15, 2001, the price of the 6.75s of May 15, 2005, was 106-211/8. Use a calculator or spreadsheet to find the yield of the bond.

3.3 Consider a 10-year par bond yielding 5%. How much of the bond's value comes from principal and how much from coupon payments? How does your answer change for a 30-year par bond yielding 5%?

3.4 Why would anyone buy a bond selling at a premium when after holding that bond to maturity it will be worth only par?

3.5 On May 15, 2001, the price and yield of the 11.625s of November 15, 2002, were 110-211/4 and 4.2139%, respectively. Say that on November 15, 2001, the yield of the bond is still 4.2139%. Calculate the annualized return on the bond over that six-month period.

3.6 Consider the following bond yields on May 15, 2001:

Bond Yield

5.25s of 8/15/2003 4.3806

5.75s of 8/15/2003 4.3838

11.125s of 8/15/2003 4.4717

Do these yields make sense relative to one another? Assume that the yield curve on May 15, 2001, was upward-sloping.

3.7 A 60-year-old retired woman is considering purchasing an annuity that pays \$25,000 every six months for the rest of her life. Assume that the term structure of semiannually compounded rates is flat at 6%.

a. If the annuity cost \$575,000 and the woman expects to live another 25 years, will she purchase the annuity? What if she expects to live another 15 years?

b. If law prohibits insurance companies from charging a different annuity price to men and to women and if everyone expects women to live longer than men, what would happen in the annuity market?

3.8 A state lottery advertises a jackpot of \$1,000,000. In the fine print it is written that the winner receives 40 annual payments of \$25,000. If the term structure is flat at 6%, what is the true value of the jackpot?