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MATH 2FM3 First Midterm
EXAMPLE EXAM
Instructor: Petar Jevtic
Duration: 50 min
McMaster University First Midterm
This test includes 16 pages and 3 questions. You are responsible for ensuring your copy
of the test is complete. Bring any discrep
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MATH 2FM3: Example Final Exam
Duration: 3h
McMaster University Final Examination
This test includes 18 pages and 8 questions. You are responsible for ensuring your copy
of the test is complete. Bring any discrepancy to the attention of your in
Family name, comma, personal name: _
Your student ID:_
UNIVERSITY OF TORONTO
ACT240H1F
ON-CHALKBOARD SICK CERTIFICATE TERM TEST 2 June 16, 2008
Instructor: Keith Sharp PhD FSA CFA
NOTES:
1. Calculators allowed
2. Its OK to write on book. If you also use s
Net present value (NPV) is the difference between the present value of cash inflows and the
present value of cash outflows, based on some compounding rate i
NPV analysis is sensitive to the reliability of future cash inflows that an investment or project
The present value of a growing annuity formula calculates the present day value of a series of
future periodic payments that grow at a proportionate rate.
A growing annuity may sometimes be referred to as an increasing annuity.
A simple example of a growi
The future value (FV) of an annuity with continuous compounding formula is used to calculate
the ending balance on a series of periodic payments that are compounded continuously.
Understanding the future value of annuity with continuous compounding formul
Text book questions for Chapters 1, 2 and 5
Chapter 1
All check point questions (answers are provided in the text book)
Questions and Problems: 1- 6, 8 - 20 (answers for the starred problems are provided in the text
book. For the remaining questions, in
Accounting and Finance (AEW)
Revision summary by Michael Prior-Jones
Cash Flow Forecast:
Description of projected incomes and expenditures over a given period.
Provides information that informs the profit & loss statement and the
balance sheet.
Balance Sh
Selected Solutions for Chapter 5 and 6 numerical problems
This document contains numerical answers for problems from Chapters 5 and 6 for
which the solutions are note provided in the text book.
CHAPTER 5
Note: Unless otherwise stated, assume that cash flo
Text book questions for Chapter 6
Check point questions: 6.2 to 6.7. (answers are provided in the text book)
Questions and Problems: 1- 7, 9 to 11, 13 to 28, 30 to 33, 36 to 39 and 43 to 45 (answers for the
starred problems are provided in the text book
Math 2FM3 Introduction to Mathematical Finance
Information Sheet (Spring 2015)
LECTURE
Monday & Wednesday 7:00-10:00 pm HH/302
May 4 to June 17, inclusive
CLASS MATERIAL: Available through Avenue to Learn (http:/avenue.mcmaster.ca/)
Instructor
Office
Phon
Cash Flow diagram; try to use this on every question
So at time 1, money is worth less (interest rate)
So PV of C1 is 100 / (1+r)
Hence,
Similarly,
100 now is worth more at time 1
FV of C0 at time 1 is 100 (1+r)
Hence,
From these formulas, we can derive:
Lecture 28
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Math 2FM3, Fall 2016, Lecture 28
7.2 Asset-Liability Matching and Immunization
To be solvable, a company will make investments so that funds will
be available to provide for outgoing payments.
Let (Lt )cfw_t>0 be the liabilities (or outgoes
Lecture 27
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Math 2FM3, Fall 2016, Lecture 27
7 Cashflow Duration and Immunization
When an investor buys a bond, there is no guarantee that yield rate
at which the bond was bought will stay the same. In fact, it will
change.
The price of the bond change
Lecture 25
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Math 2FM3, Fall 2016, Lecture 25
Ch. 6 The term structure of interest rates
In reality time to maturity yield changes over time with respect to
both maturity and current time due to many economical factors.
The relationship between time to m
Lecture 26
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Math 2FM3, Fall 2016, Lecture 26
6.3. Forward rates of interest
n-year forward rate is the interest that should be charged for a one
year loan that begins n years from now and lasts 1 year. The n-year
forward rate in,n+1 is the interest rate
Lecture 23
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Math 2FM3, Fall 2016, Lecture 23
5.1.4 Alternative Methods of Valuing Investments
Returns
Capital budgeting is the management process of evaluating
alternative investment opportunities. Two models of capital
budgeting we have already seen: i
Lecture 24
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Math 2FM3, Fall 2016, Lecture 24
5.2 Dollar Weighted and time weighted rate of return
Managers of investment funds have to report the return of their
fund on an annual basis.
5.2.1 Dollar-Weighted Rate of return
Dollar-weighted rate of retu
Lecture 22
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Math 2FM3, Fall 2016, Lecture 22
Ch. 5 Measuring The Rate of Return of an Investment
The valuation rate at which a present value is calculated can be a
meaningful measure of the rate of return earned by the lender or
paid by the borrower, an
Name:
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MATH 2FM3 Second Midterm (Example Exam)
Instructor: Petar Jevtic
Duration: 50 min
McMaster University Second Midterm
This test includes 8 pages containing instructions, questions, solutions and formula sheet.
You are responsible for ensuring y
Derivative instruments (or simply derivatives) are a category of financial instruments that
includes options, futures, forwards and swaps
While there is general agreement among financial practitioners as to which instruments are
considered derivatives and
Lecture 2.1
0-0
Math 2FM3 Spring 2015
1.5 Eective and Nominal Rates of Discount
So far, all interest amounts were paid or charged at the end of the compounding period. Interest payable in arrears is the standard way.
However, in some transactions intere
Math 2FM3, Fall 2015, Lecture 5
1.6 The Force of Interest
Let us again consider a continuous-time framework, i.e. nancial transaction take place
in a continuum of time.
Let A(t) denote again the accumulated value of an investment at time t. The amount
1
Math 2FM3, Fall 2015, Lecture 7
Ch. 2 Valuation of Annuities
Many nancial transactions involve a series of payments (cash ows). For example:
dividend payments on a stock, monthly payment on a loan, or annual interest payments
on a coupon bond.
The gener
Math 2FM3, Fall 2015, Lecture 2
(Section 1.1. continued)
1.1.3 Simple Interest
For a short period of time, simple interest is often considered, instead of compound
interest. At an interest rate of i per year, 1 grows to 1 + i at the end of one year. If t
Math 2FM3, Fall 2015, Lecture 8
2.1.2 Present Value of an Annuity
Example: You want to open a saving account with a single deposit today so that you
can withdraw 1000 per year for 4 years, starting 1 year from now. Find the amount you
have to deposit if
Math 2FM3, Fall 2015, Lecture 9
2.1.3 Annuity Immediate and Annuity Due
Valuation of a level series of equally spaced payments (i.e. annuity) depends on : 1) the
number of payments. 2) the valuation point. 3) the interest rate per payment.
So far we had
Lecture 19
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Math 2FM3, Fall 2016, Lecture 19
4.1.3 Bond Prices between Coupon Dates
In practice bonds are traded daily not only before the coupon
payments.
Regard coupon period as unit of time and find the price of a bond
Pt , 0 t 1 with t measured fro
Lecture 21
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Math 2FM3, Fall 2016, Lecture 21
4.3 Applications and Illustrations
4.3.1 Callable Bond: Optional Redemption Dates
A bond issuer adds flexibility by specifying a range of dates during
which redemption may occur at issuers option. Such a bond
Lecture 20
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Math 2FM3, Fall 2016, Lecture 20
4.2 Amortization of a bond
Let us determine the amount of interest received and principal
returned on a bond coupon or redemption payment. This is
important for taxation and accounting purposes.
For a bond o
Lecture 18
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Math 2FM3, Fall 2016, Lecture 18
Ch. 4 Bond Valuation
To borrow large amounts over longer terms a government or
corporation can issue a bond, which is a debt that calls for periodic
interest payments, called coupons, and the return of the pr
Lecture 17
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Math 2FM3, Fall 2016, Lecture 17
3.4 Applications and Illustrations
Let us consider again the case of a loan with principal repaid after n
periods, the sequence of payments received by the lender is L i
(n 1) times and L + L i in the end. Su