Question

Malia must decide whether to buy a one-year bond today and another one a year from now or buy a two-year bond today. In which of the following scenarios is she better off taking the first action? The second action?

a. This year, the interest on a one-year bond is 4%; next year, it will be 10%. The interest rate on a two-year bond is 5%.

b. This year, the interest rate on a one-year bond is 4%; next year, it will be 1%. The interest rate on a two-year bond is 3%.

Short answer

Malia is better off taking the first course of action in case of option a.

Malia is better off taking the second course of action in case of option b.

Step-by-step solution

Explanation for part (a)

The interest rate on a one-year bond for a given year is 4%. However, the interest rates are likely to increase to 10% from next year.Thus, if Malia invests in a two-year bond, she will incur a loss since she will get an interest of 5% on two-year bonds. On the other hand, if she invests in one-year bonds each year, then she will earn an average rate of interest equal to;

$$\begin{gathered} \frac{\text{r1 + r2}}{\text{2}} \\ \frac{\text{4 + 10}}{\text{2}}\text{= 7\%} \end{gathered}$$

This is more than 5%. Therefore, Malia should take the first action in this case.

Explanation for part (b)

The interest rate in the first year for one-year bonds is 3%, and next year the interest rates are likely to fall to 1%. Therefore, if Malia invests in one-year bonds each year, she will earn an annual rate of interest equal to;

$$\begin{gathered} \frac{\text{r1 + r2}}{\text{2}} \\ \frac{\text{4 + 1}}{\text{2}}\text{= 2.5\%} \end{gathered}$$

However, the interest on two-year bonds is 3%, which is more than 2.5%. Thus, Malia must take the second action in this scenario.