Chapter 2, Problem 8P

Summary Introduction

To determine: The current rate of one-year, two-year, three-year and four-year treasury security.

Answer to Problem 8P

The current rate of one-year is 6%, two-year is 6.50%, three-year is 6.83% and four-year treasury security is 7.09%.

Explanation of Solution

Determine the current rate of one-year and two-year treasury security

The current rate of one-year treasury security is already given, which is 6%.

$\begin{array}{c}CurrentRat{e}_{2-Year}=\left[{\left(\left(1+Rat{e}_{Year1}\right)\times \left(1+ExpectedRat{e}_{Year2}\right)\right)}^{\left(\frac{1}{n}\right)}-1\right]\\ =\left[{\left(\left(1+6\%\right)\times \left(1+7\%\right)\right)}^{\left(\frac{1}{2}\right)}-1\right]\\ =\left[1.064988-1\right]\\ =0.064988or6.50\%\end{array}$

Therefore, the current rate of two-year treasury security is 6.50%.

Determine the current rate of three-year treasury security

$\begin{array}{c}CurrentRat{e}_{3-Year}=\left[{\left(\begin{array}{l}\left(1+Rat{e}_{Year1}\right)\times \left(1+ExpectedRat{e}_{Year2}\right)\times \\ \left(1+ExpectedRat{e}_{Year3}\right)\end{array}\right)}^{\left(\frac{1}{n}\right)}-1\right]\\ =\left[{\left(\left(1+6\%\right)\times \left(1+7\%\right)\times \left(1+7.50\%\right)\right)}^{\left(\frac{1}{3}\right)}-1\right]\\ =\left[1.068315-1\right]\\ =0.068315or6.83\%\end{array}$

Therefore, the current rate of three-year treasury security is 6.83%.

Determine the current rate of four-year treasury security

$\begin{array}{c}CurrentRat{e}_{3-Year}=\left[{\left(\begin{array}{l}\left(1+Rat{e}_{Year1}\right)\times \left(1+ExpectedRat{e}_{Year2}\right)\times \\ \left(1+ExpectedRat{e}_{Year3}\right)\times \left(1+ExpectedRat{e}_{Year4}\right)\end{array}\right)}^{\left(\frac{1}{n}\right)}-1\right]\\ =\left[{\left(\left(1+6\%\right)\times \left(1+7\%\right)\times \left(1+7.50\%\right)\times \left(1+7.85\%\right)\right)}^{\left(\frac{1}{4}\right)}-1\right]\\ =\left[1.070852-1\right]\\ =0.070852or7.09\%\end{array}$

Therefore, the current rate of four-year treasury security is 7.09%.

Summary Introduction

To determine: The yield curve for the current rate.

Explanation of Solution

The yield curve is as follows: