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
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 (
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 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
STAT2032/6046 - Solutions to Selected Questions - Lecture
Week 4
1. A company will receive a perpetuity of $50,000 per annum. The rst
payment under this agreement is due at t = 10. What is the present value
of this agreement at t = 0, assuming an annual i
STAT2032/6046 - Solutions to Additional Questions Lecture Week 8
1. A 91-day Government Bill with a par-value of $100 is being oered at
$98.56. What is the corresponding simple annual rate of discount for this
security?
Solve the following equation for d:
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
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
THE AUSTRALIAN NATIONAL UNIVERSITY
SCHOOL OF FINANCE AND APPLIED STATISTICS
Mid-Semester Examination 2009
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
Study Period: 10 minutes
Time Allowed: 11/2 hours
Permitted Material:
Non-Programmable Calculators
Dict
THE AUSTRALIAN NATIONAL UNIVERSITY
SCHOOL OF FINANCE, ACTUARIAL STUDIES AND
APPLIED STATISTICS
Mid-Semester Examination 2010
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
Study Period: 10 minutes
Time Allowed: 11/2 hours
Permitted Material:
Non-Programmab
STAT2032/6046:
Financial Mathematics
Bronwyn Loong
Lectures Week 7
Capital budgeting - comparing investment projects
Criteria for comparison:
Accumulated prot
Net present value
Internal rates of return
Discounted payback period
Accumulated prot
Let ct
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 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 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 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 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
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
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 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
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
THE AUSTRALIAN NATIONAL UNIVERSITY
SCHOOL OF FINANCE, ACTUARIAL STUDIES AND
APPLIED STATISTICS
Mid-Semester Examination 2010
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
Study Period: 10 minutes
Time Allowed: 11/2 hours
Permitted Material:
Non-Programmab
THE AUSTRALIAN NATIONAL UNIVERSITY
SCHOOL OF FINANCE AND APPLIED STATISTICS
Mid-Semester Examination 2009
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
Study Period: 10 minutes
Time Allowed: 11/2 hours
Permitted Material:
Non-Programmable Calculators
Dict
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
TUTORIAL SOLUTIONS WEEK 4
Question 1
12 payments of $2,000 each are made at 2-year intervals. Find the value of the series
(a) 2 years before the first payment at annual effective interest rate i = 0.08 ,
(b)