M&B3 3rd Edition by Dean Croushore

Exercise 18

Compare a two-year bond with two successive one-year bonds in a situation in which an investor buys a one-year bond today and then another one-year bond when the fi rst matures. Suppose that the two-year bond has an interest rate of 8 percent each year.
a Now 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 he has at the end of the two years. In each case, how much would an investor have at the end of two years if he invested $1,000 today
(i) The one-year interest rate today is 7 percent; the one-year interest rate will be 9 percent one year from now.
(ii) The one-year interest rate today is 5 percent; the one-year interest rate will be 11 percent one year from now.
(iii) The one-year interest rate today is 3 percent; the one-year interest rate will be 13 percent one year from now.
(iv) The one-year interest rate today is 0 percent; the one-year interest rate will be 16 percent one year from now.
b From these results, is it reasonable to compare the average interest rates on alternative fi nancial investments (In other words, how reasonable is the assumption that we can compare average interest rates on short-term bonds with the interest rate on long-term bonds instead of using the exact method )