University of Waterloo
ACTSC231 - Mathematics of Finance
Winter 2012
Tutorial #2
1. Complete the following table that summarizes the key relationships for simple accumulation:
Rate
Accumulated value of
1 at time t, a(t)
Present value of
1 at time t, v (t)
University of Waterloo
ACTSC231 - Mathematics of Finance
Winter 2012
Problem Set #1
1. Suppose that the accumulation function of an account is given by a(t) = t2 + 0.1t + , and the
eective interest rate i2 for the second year is 11.72%. Find
a) Find and .
1 . ( 6pts.) A rthur b uys $ 2,100 w orth o f s tock. S ix m onths l ater, t he v alue o f t he s tock has r isen t o $ 2,200 a nd A rthur b uys a nother $ 900 w orth o f s tock. A fter a .notherg $ months, A rthur's h oldings a .rew orth $ 3,000 a nd h e
Assignment 3
ACTSC231 (Mathematics of Finance), FALL 2010
This assignment consists of two parts. In the rst part, you need to work out eleven questions that are in the same style as in the previous two assignments. In the second part, you need to use Exce
Assignment 2
ACTSC231 (Mathematics of Finance), Winter 2010
Due: February 11 (Friday)
Hand in to the instructor in class
To earn the credit of the assignment, you need to justify your answer. Simply listing the nal
answer is unacceptable. I might only sel
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Actsc 231 - Problem Set 7 Solution
This problem set is composed mainly of recommended problems from the course textbook.
For the textbook problems, at the beginning of the question, a reference will be made to the
exercise from which it was taken.
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Actsc 231 Notes
1
1.1
Chapter 1 - The Time Value of Money
Introduction
Interest can be defined as the compensation one receives for lending an asset. For example,
? if you deposit money in a bank account, then the banking institution can do anything with
Chapter 1. The Growth of Money
ACTSC 231 Mathematics of Finance
Department of Statistics and Actuarial Science
University of Waterloo
Instructor: Fan Yang
Fan Yang ( UWaterloo )
Chapter 1
1 / 33
Interest
(p10) Interest is the payment by a borrower to a le
Chapter 3. Annuities (Certain)
ACTSC 231 Mathematics of Finance
Department of Statistics and Actuarial Science
University of Waterloo
Instructor: Fan Yang
Fan Yang ( UWaterloo )
Chapter 3
1 / 48
Definition of general annuities (p109-110)
An annuity is a r
University of Waterloo
ACTSC231 - Mathematics of Finance
Winter 2012
Quiz #4 Solution
First Name:
Last Name:
UW ID #:
Permitted aids:
Date:
Time:
SOA approved or equivalent calculator
Monday, March 5, 2012
50 minutes, 3:30pm 4:20pm
Instructions:
1. Clearl
University of Waterloo
ACTSC231 - Mathematics of Finance
Winter 2012
Quiz #3
First Name:
Last Name:
UW ID #:
Permitted aids:
Date:
Time:
SOA approved or equivalent calculator
Monday, February 13, 2012
50 minutes, 3:30pm 4:20pm
Instructions:
1. Clearly ind
University of Waterloo
ACTSC231 - Mathematics of Finance
Winter 2012
Quiz #2
First Name:
Last Name:
UW ID #:
Permitted aids:
Date:
Time:
SOA approved or equivalent calculator
Monday, January 30, 2011
50 minutes, 3:30pm 4:20pm
Instructions:
1. Clearly indi
University of Waterloo
ACTSC231 - Mathematics of Finance
Winter 2012
Tutorial #4
1. For time t > 0, the discount function is dened as
1
1 + 0.01t
A 5 year annuity has payments of 1 at times t = 1, 2, 3, 4, 5. John Doe calculates the present value
of this
University of Waterloo
ACTSC231 - Mathematics of Finance
Winter 2012
Tutorial #6
1. Consider a 2 year $1000 par-value bond with 10% annual coupons where the one year and two
years spot rates are r1 = 0.07 and r2 = 0.08.
a) If this bond sells for $1040, de
University of Waterloo
ACTSC231 - Mathematics of Finance
Winter 2012
Tutorial #5
1. Payments are made into an account continuously at a rate of 8Y + tY per year, for 0 t 10.
At time T = 10, the account is worth $20,000. Find Y if the account earns interes
University of Waterloo
ACTSC231 - Mathematics of Finance
Winter 2012
Tutorial #4
1. For time t > 0, the discount function is dened as
1
1 + 0.01t
A 5 year annuity has payments of 1 at times t = 1, 2, 3, 4, 5. John Doe calculates the present value
of this
University of Waterloo
ACTSC231 - Mathematics of Finance
Winter 2012
Tutorial #3
1. Jane Doe wishes to accumulate $250000 in a college fund at the end of 18 years. If she deposits
$10000 in the fund at the beginning of each of the rst nine years and $X at
University of Waterloo
ACTSC231 - Mathematics of Finance
Winter 2012
Tutorial #1
1. Given that a(t) = 1 + max(0, e(t) t, with = 0.9, complete the following table:
t e(t) a(t) it
0
1
1 0.03
2 0.04
3 0.02
4 -0.05
5 -0.04
dt
2. Consider a bank account that c
Examples for Chapter 7
ACTSC 231 Mathematics of Finance
Department of Statistics and Actuarial Science
University of Waterloo
Instructor: Fan Yang
Fan Yang ( UWaterloo )
Chapter 7
1/6
1. (SOA, May, 2003, #26) 1000 is deposited into Fund X, which earns
an
Chapter 6. Bonds
ACTSC 231 Mathematics of Finance
Department of Statistics and Actuarial Science
University of Waterloo
Instructor: Fan Yang
Fan Yang ( UWaterloo )
Chapter 6
1 / 20
Alphabet soup of bonds
A bond is a debt instrument; it is a form of loan,
Chapter 2 Examples
ACTSC 231 Mathematics of Finance
Department of Statistics and Actuarial Science
University of Waterloo
Instructor: Fan Yang
Fan Yang ( UWaterloo )
Chapter 2
1/6
Example 1
0.1
1. (SOA, Nov., 1993, #2) At a force of interest t = 1+0.1t
,
Examples for Chapter 6
ACTSC 231 Mathematics of Finance
Department of Statistics and Actuarial Science
University of Waterloo
Instructor: Fan Yang
Fan Yang ( UWaterloo )
Chapter 5
1/7
1. A 10,000 par value 10-year bond with 8% annual coupons is bought
at
Chapter 3. Simple Annuities
ACTSC 231 Mathematics of Finance
Department of Statistics and Actuarial Science
University of Waterloo
Instructor: Fan Yang
Fan Yang ( UWaterloo )
Chapter 3
1 / 18
Definition of general annuities
An annuity is a regular series