Quality Learning Support For All
First time here? Checkout the FAQs!
x

*Math Image Search only works best with SINGLE, zoomed in, well cropped images of math. No selfies and diagrams please :)

For Example

Math Image Search 1
Math Image Search 2

Join the MathsGee Club for exclusive quizzes, courses and interactive content without ads.



ASK - ANSWER - COMMENT - VOTE - CREATE


Sites: Global Q&A | Wits | MathsGee Club | Joburg Libraries | StartUps | Zimbabwe | OER

MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

0 like 0 dislike
12 views
Bonds pay annual coupons at a rate of \(6 \%\) per annum, in arrear, and are redeemable at par. The bonds, redeemable in exactly one, two, three, four and five years respectively, are all priced at R 96 per R100 nominal.
i. Determine the one-year, two-year and three-year spot rates.
[3]
ii. Calculate \(f_{0,1}, f_{1,2}\) and \(f_{2,2}\) where \(f_{t, r}\) is the annual forward interest rate agreed at time 0 for an investment made at time \(t\) (where \(t>0\) ) for a period of \(r\) years.
iii. Comment on the term structure of the spot rates in i. with reference to expectations theory.
in Actuarial Science by Platinum (91,198 points) | 12 views

1 Answer

0 like 0 dislike
(i)
\[
106\left(1+y_{1}\right)^{-1}=96
\]
\[
y_{1}=0.1041666
\]
\[
106\left(1+y_{2}\right)^{-2}+6\left(1+y_{1}\right)^{-1}=96 \Rightarrow 106\left(1+y_{2}\right)^{-2}+6(1+0.104167)^{-1}=96
\]
\[
106\left(1+y_{2}\right)^{-2}=90.56604
\]
\[
y_{2}=0.081858
\]
\[
106\left(1+y_{3}\right)^{-3}+6\left(1+y_{2}\right)^{-2}+6\left(1+y_{1}\right)^{-1}=96
\]
\[
106\left(1+y_{3}\right)^{-3}=85.43965824
\]
\[
y_{3}=0.074522
\]

(ii)
\[
\begin{aligned}
&f_{0,1}=y_{1}=10.41666 \% \\
&\left(1+f_{1,2}\right)^{2}=\frac{\left(1+y_{3}\right)^{3}}{\left(1+y_{1}\right)}=\frac{(1+0.074522)^{3}}{(1+0.1041666)}=1.1236
\end{aligned}
\]
\[
f_{1,2}=0.06
\]
\[
106\left(1+y_{4}\right)^{-4}+6\left(1+y_{3}\right)^{-3}+6\left(1+y_{2}\right)^{-2}+6\left(1+y_{1}\right)^{-1}=96
\]
\[
\begin{aligned}
&\left(1+y_{4}\right)^{-4}=\frac{80.60345}{106}=0.760409917 \\
&\left(1+f_{2,2}\right)^{2}=\frac{\left(1+y_{4}\right)^{4}}{\left(1+y_{2}\right)^{2}}=\frac{(0.760409917)^{-1}}{(1+0.08185797)^{2}}=1.1236 \\
&f_{2,2}=0.06
\end{aligned}
\]
(iii)
- Spot rates are a decreasing function of the term.
- The expectations theory posits that investors are expecting a decrease in short term spot rates.
- This makes short-term investments less attractive and longer-term investments more attractive.
- In these circumstances, yields on short-term investments will rise and yields on longterm investments will fall.
by Platinum (91,198 points)

Related questions

Join the MathsGee Answers & Explanations community and get study support for success - MathsGee Answers & Explanations provides answers to subject-specific educational questions for improved outcomes.



On MathsGee Answers & Explanations, you can:


  1. Ask questions
  2. Answer questions
  3. Comment on Answers
  4. Vote on Questions and Answers
  5. Donate to your favourite users
  6. Create/Take Live Video Lessons

Posting on MathsGee Answers & Explanations


  1. Remember the human
  2. Behave like you would in real life
  3. Look for the original source of content
  4. Search for duplicates before posting
  5. Read the community's rules

Join the MathsGee Club for exclusive quizzes, courses and interactive content without ads.



Wits Maths Questions

What would the 9 steps be to consider when creating a digital marketing strategy
Posted on Friday October 01, 2021

Nine important decisions to consider when developing a digital marketing strategy

Click Here To Read More.
 

Is the IMM Study Group platform easy to use?
Posted on Friday October 01, 2021

Is the IMM Study Group platform easy to use?

A grain company called Splitting My Grain analyses and tabulates the number of sales it fulfilled in 2020 in the table below:
Posted on Thursday September 30, 2021

A grain company called Splitting My Grain analyses and tabulates the number of sales it fulfilled in 2020 in the table below:

\[
\begin{array}{l|l|l|l|}
\hline {\text { Product }} & {\text {...

Click Here To Read More.
 

An online book shop called Paper Cut collects its home delivery data for its Gauteng depot, which is located in Boksburg.
Posted on Thursday September 30, 2021

An online book shop called Paper Cut collects its home delivery data for its Gauteng depot, which is located in Boksburg.

\[
\begin{array}{lll|}
\hline \text { Destination address city } &...

Click Here To Read More.
 

Bongani owns and operates a fuel garage. He compiled the table below showing the number of litres of each type of fuel sold per month in 2020 .
Posted on Thursday September 30, 2021

Bongani owns and operates a fuel garage. He compiled the table below showing the number of litres of each type of fuel sold per month in 2020 .

\[
\begin{array}{llll|}
\hline...

Click Here To Read More.
 

MathsGee Tools

Math Worksheet Generator

Math Algebra Solver

Trigonometry Simulations

Vectors Simulations

Matrix Arithmetic Simulations

Matrix Transformations Simulations

Quadratic Equations Simulations

Probability & Statistics Simulations

PHET Simulations

Visual Statistics

Join the MathsGee Club for exclusive quizzes, courses and interactive content without ads.



Management Leadership | MathsGee ZOOM | eBook

Join the MathsGee Club for exclusive quizzes, courses and interactive content without ads.