STAT2032/6046 - Solutions to Mid-Semester Examination First Semester 2013
1
Question 1 (12 marks)
(a) (i) [2 marks] Show that at a nominal interest rate of i(m) per annum
convertible m times per year, the total amount of interest earned in a year
on an in
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
TUTORIAL SOLUTIONS WEEK 5
Question 1
Calculate values for the following functions:
a) a7 at interest rate of 7.5% per annum effective.
b) Ia 5 at interest rate of 10% per annum effective.
s (4)
c) 15 at a nomi
STAT2032/6046 - Solutions to Selected Questions - Lecture
Week 5
1. For a price of $100, you receive monthly interest payments of $1 in
arrears for 5 years and a lump sum payment of $X at the end of 5 years.
Assuming an eective annual rate of interest of
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
TUTORIAL SOLUTIONS WEEK 3
Question 1
Find the present value of 1000 due at the end of 10 years if
(a) i (2) = 0.09 , (b) i (6) = 0.09 , and (c) i (12) = 0.09 .
Solution
mt
i (m)
S (0) = S (t )(1 + i ) = S (
Australian National University
Research School of Finance, Actuarial Studies and
Applied Statistics
STAT2032/6046: Financial Mathematics
Review Questions (Week 1 Week 3)
WEEK 1
Question 1
At a certain rate of simple interest $1100 will accumulate to $1250
FINANCIAL MATHEMATICS
STAT 2032 / STAT 6046
LECTURE NOTES WEEK 5
EQUATIONS OF VALUE
Cash flow models were briefly introduced in week 1. Recapping, in a cash flow model
payments received are income and are positive cash flows. Payments made are outgo and a
FINANCIAL MATHEMATICS
STAT 2032 / STAT 6046
LECTURE NOTES WEEK 3
SUMMARY OF FORMULAE
The important relationships between the variables introduced so far are given below. These
also appear on page 1 of the formula sheet that you will have available for the
FINANCIAL MATHEMATICS
STAT 2032 / STAT 6046
LECTURE NOTES WEEK 6
LOAN REPAYMENTS
A common transaction involving compound interest is a loan that is repaid by regular
instalments, at a fixed rate of interest, for a predetermined term.
Repayments can be dec
Australian National University
Research School of Finance, Actuarial Studies and
Applied Statistics
STAT2032/6046: Financial Mathematics
Review Questions (Week 4 Week 6)
WEEK 4
Question 1
Evaluate the following at i = 15%
a.
b. Ia60
c. Ia 60
d. Is 60
Solu
Australian National University
Research School of Finance, Actuarial Studies and
Applied Statistics
STAT2032/6046: Financial Mathematics
Review Questions (Week 7 Week 9)
WEEK 7
Question 1
Deposits of $1100 are made into an investment fund at year 0 and ye
Australian National University
Research School of Finance, Actuarial Studies and
Applied Statistics
STAT2032/6046: Financial Mathematics
Review Questions (Week 1 Week 3)
WEEK 1
Question 1
At a certain rate of simple interest $1100 will accumulate to $1250
FINANCIAL MATHEMATICS
STAT 2032 / STAT 6046
LECTURE NOTES WEEK 9
CALCULATING YIELDS
If the investor is not subject to taxation the yield is referred to as a gross yield. If the investor
is subject to taxation the yield is referred to as a net yield.
As st
FINANCIAL MATHEMATICS
STAT 2032 / STAT 6046
LECTURE NOTES WEEK 10
ARBITRAGE AND FORWARD CONTRACTS
Arbitrage is the simultaneous buying and selling of two economically equivalent but
differentially priced portfolios so as to make risk-free profit. For exam
FINANCIAL MATHEMATICS
STAT 2032 / STAT 6046
LECTURE NOTES WEEK 12
STOCHASTIC INTEREST RATE MODELS
So far we have taken a deterministic approach, where it was assumed that interest rates used
in a financial transaction have been known in advance.
Although
FINANCIAL MATHEMATICS
STAT 2032 / STAT 6046
LECTURE NOTES WEEK 8
FIXED INTEREST SECURITIES
Governments and corporations will often wish to raise or borrow money from investors to
fund their spending plans. They may wish to repay the money in the near futu
FINANCIAL MATHEMATICS
STAT 2032 / STAT 6046
LECTURE NOTES WEEK 7
MEASURING INVESTMENT PERFORMANCE
It is often necessary to be able to measure the investment performance of a fund over a
period.
Fund value will go up or down as a result of changes in:
Inc
Australian National University
Research School of Finance, Actuarial Studies and
Applied Statistics
STAT2032/6046: Financial Mathematics
Review Questions (Week 7 Week 9)
WEEK 7
Question 1
Deposits of $1100 are made into an investment fund at year 0 and ye
Australian National University
Research School of Finance, Actuarial Studies and
Applied Statistics
STAT2032/6046: Financial Mathematics
Review Questions (Week 4 Week 6)
WEEK 4
Question 1
Evaluate the following at i = 15%
a.
b. Ia60
c. Ia 60
d. Is 60
Ques
Australian National University
Research School of Finance, Actuarial Studies and
Applied Statistics
STAT2032/6046: Financial Mathematics
Review Questions (Week 10 Week 12)
WEEK 10
Question 1
On 1 January 1999 an investor agrees to pay $3,000 in four years
STAT2032/6046 - Solutions to Additional Questions Lecture Week 1
1. An investment of $50 grows to $X at an effective simple rate of 10% per annum.
After 20 years the value of this investment is:
a. $250.00
b. $145.00
c. $336.37
d. $150.00
Answer=d. X = 50
STAT2032/6046 - Solutions to Additional Questions Lecture Week 3
1. A debt collection agency pays a doctor $5,000 for invoices that the doctor has not
been able to collect on. After two years, the collection agency has collected $6,000
on the invoices. At
FINANCIAL MATHEMATICS
STAT 2032 / STAT 6046
LECTURE NOTES WEEK 1
CASH FLOW MODELS
A cash flow model is a mathematical projection of payments arising from a financial
contract or block of contracts.
Payments received are income and are positive cash flows.
FINANCIAL MATHEMATICS
STAT 2032 / STAT 6046
LECTURE NOTES WEEK 2
NOMINAL RATES OF INTEREST
For contracts where interest payments are credited or compounded more frequently than once
a year, eg monthly, some financial institutions will think in terms of an
FINANCIAL MATHEMATICS
STAT 2032 / STAT 6046
LECTURE NOTES WEEK 3
SUMMARY OF FORMULAE
The important relationships between the variables introduced so far are given below. These
also appear on page 1 of the formula sheet that you will have available for the
STAT 2032/6046:
Financial Mathematics
Abhinav Mehta
Week 2
Question
What deposit made today will provide for a payment of $1000 in
1 year and $2000 in 3 years, if the effective compound rate of
interest is 7.5% pa?
The present value of the 2 payments is:
FINANCIAL MATHEMATICS
STAT 2032 / STAT 6046
LECTURE NOTES WEEK 4
PERPETUITIES
An annuity where payments continue forever is called a perpetuity.
The present value of a perpetuity where 1 is payable at the end of each year (in arrears or
immediate perpetui
FINANCIAL MATHEMATICS
STAT 2032 / STAT 6046
LECTURE NOTES WEEK 11
INTEREST RATE RISK
We will now cover simple measures used to quantify the level of vulnerability of
fixed interest securities to interest rate movements, and we will also introduce the
tech
AUSTRALIAN NATIONAL UNIVERSITY
First Semester Final Examination 2007
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
SOLUTIONS
Question One (15 marks)
a)
b)
Find the accumulated value at the date of the final payment of $50 paid at the end
of each year for
THE AUSTRALIAN NATIONAL UNIVERSITY
RESEARCH SCHOOL OF FINANCE, ACTUARIAL STUDIES AND
APPLIED STATISTICS
Final Examination, Semester 2, 2015
STAT2032/6046
FINANCIAL MATHEMATICS
Study Time: 15 minutes
Writing Time: 3 hours
Permitted materials:
Paper Based D
THE AUSTRALIAN NATIONAL UNIVERSITY
SCHOOL OF FINANCE AND APPLIED STATISTICS
First Semester Final Examination 2008
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
Study Period: 15 minutes
Time Allowed: 3 hours
Permitted Material:
Non-Programmable Calculators
Australian National University
Research School of Finance, Actuarial Studies and
Applied Statistics
STAT2032/6046: Financial Mathematics
Review Questions (Week 10 Week 12)
WEEK 10
Question 1
On 1 January 1999 an investor agrees to pay $3,000 in four years
THE AUSTRALIAN NATIONAL UNIVERSITY
SCHOOL OF FINANCE, ACTUARIAL STUDIES AND
APPLIED STATISTICS
First Semester Final Examination 2012
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
Study Period: 15 minutes
Time Allowed: 3 hours
Permitted Material:
Non-Progr
THE AUSTRALIAN NATIONAL UNIVERSITY
SCHOOL OF FINANCE AND APPLIED STATISTICS
First Semester Final Examination 2008
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
Study Period: 15 minutes
Time Allowed: 3 hours
Permitted Material:
Non-Programmable Calculators