Compare a two-year bond with two successive one-year bonds, in which an investor buys a one-year bond today, then another one-year bond when the first matures. Suppose the two-year bond has an annual interest rate of 4 percent.Consider the pattern of interest rates on the one-year bonds listed below and explain whether an investor should buy the two-year bond or the one-year bond today, assuming that the only thing that matters to the investor is the amount of money she has at the end of the two years; that is, she is risk neutral. In each case, how much would an investor have at the end of two years if she invested $1,000 today? Show your work. Round to the nearest penny ($0.01). In each case be sure to say which bond the investor would buy today.
a.The interest rate on a one-year bond today is 1 percent, and the interest rate on a one-year bond purchased in one year from now is 8 percent. b.The interest rate on a one-year bond today is 2 percent; and the interest rate on a one-year bond purchased one-year from now is 6 percent. c.The interest rate on a one-year bond today is 3 percent; and the interest rate on a one-year bond purchased one-year from now is 5 percent. d.The interest rate on a one-year bond today is 5 percent; nd the interest rate on a one-year bond purchased one-year from now is 3 percent.
What will be an ideal response?
| a. | Two one-year bonds: | $1,000 × 1.01 × 1.08 = $1,090.80 |
| One two-year bond: | $1,000 × 1.042 = $1,081.60 | |
| In this case, the investor will purchase two one-year bonds. | ||
| b. | Two one-year bonds: | $1,000 × 1.02 × 1.06 = $1,081.20 |
| One two-year bond: | $1,000 × 1.042 = $1,081.60 | |
| In this case, the investor will purchase one two-year bond. | ||
| c. | Two one-year bonds: | $1,000 × 1.03 × 1.05 = $1,081.50 |
| One two-year bond: | $1,000 × 1.042 = $1,081.60 | |
| In this case, the investor will buy either two one-year bonds or one two-year bond. | ||
| d. | Two one-year bonds: | $1,000 × 1.05 × 1.03 = $1,081.50 |
| One two-year bond: | $1,000 × 1.042 = $1,081.60 | |
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