Extended Euclids Algorithm
The extended Euclids algorithm can be used to express gcd(a, b) as an integer linear combination of a and b, i.e., we can use it to nd integers x and y such that
ax + by = gcd(a, b).
Lets illustrate it by nding integers x and y

Review of Eigenvalues and Eigenvectors
Gilles Cazelais
An eigenvector of a square matrix A is a nonzero satisfy
vector K such that
1
x = 1 t, y = 2 t, z = t, for any t = 0.
2
AK = K
By choosing t = 2, we obtain the eigenvector
for some number called an ei

Euclids Algorithm
Euclids algorithm to nd the greatest common divisor of two integers is based on the following lemma.
Lemma If a = bq + r where a, b, q, and r are integers, then gcd(a, b) = gcd(b, r).
Proof. Since gcd(a, b) divides both a and b, then it

MATH 2600/STAT 2600, Theory of Interest
FALL 2010
Toby Kenney
Homework Sheet 1
Due: Thursday 30th September: 1:00 PM
1. Calculate the accumulated value on maturity of the following investments:
(a) $1,000 invested for 3 months at 5% simple interest.
(b) $

MATH 2600/STAT 2600, Theory of Interest
FALL 2010
Toby Kenney
Homework Sheet 7
Due: Thursday 2nd December
1. A machine has a current cost of $40,000. The machine has an expected
lifetime of 20 years. It cannot be resold when it is nished with. The
maintai

MATH 2600/STAT 2600, Theory of Interest
FALL 2010
Toby Kenney
Homework Sheet 5
Model Solutions
1. A loan of $4,000 at j12 = 8% is amortised with equal monthly payments
for 6 months, with the rst payment in one month.
(a) Calculate the monthly payments.
(b

MATH 2600/STAT 2600, Theory of Interest
FALL 2010
Toby Kenney
Homework Sheet 2
Due: Thursday 7th October: 1:00 PM
1. Calculate the accumulated value on maturity of $1,000 invested for 23
years at 5% interest compounded:
(a) annually.
(b) monthly.
2. Which

MATH 2600/STAT 2600, Theory of Interest
FALL 2010
Toby Kenney
Homework Sheet 3
Due: Thursday 14th October: 1:00 PM
1. Ms. Jones invests $500 a month in her pension plan, which pays interest at
j12 = 6%. She makes her rst investment on her 21st bithday. Ho

MATH 2600/STAT 2600, Theory of Interest
FALL 2010
Toby Kenney
Homework Sheet 6
Due: Thursday 25th November.
1. Calculate the price that should be paid for each of the following bonds to
obtain the desired yield:
(a) face value $5,000, maturing at par in 1

MATH 2600/STAT 2600, Theory of Interest
FALL 2010
Toby Kenney
Homework Sheet 4
Due: Thursday 21st October: 1:00 PM
1. John makes a deposit of $2,000 at the end of every year into an account
that pays interest at j12 = 5%. How much is in the account at the

MATH 2600/STAT 2600, Theory of Interest
FALL 2013
Toby Kenney
Sample Midterm Examination
Time allowed 1 hour 20 minutes
1. Mr. Almon receives an invoice for $4,000, for payment within 50 days.
He can get a 2% discount if he pays within the rst 10 days. Wh

MATH 2600/STAT 2600, Theory of Interest
FALL 2013
Toby Kenney
Midterm Examination
Model Solutions
1. Mr and Mrs. Allen are saving up for their childrens education. They
have two children, aged 9 and 11. They invest $40,000 today at j1 = 8%
interest, and t

MATH 2600/STAT 2600, Theory of Interest
FALL 2013
Toby Kenney
Midterm Examination
Thursday 17th October: 10:3511:25 AM
You may use a scientic calculator, but not a programmable or a nancial
calculator for this examination.
1. Mr and Mrs. Allen are saving

MATH 2600/STAT 2600, Theory of Interest
FALL 2013
Toby Kenney
Practice Final Examination
This Sample Examination has more questions than the actual nal, in order to cover a wider range of questions. Estimated times are given after each
question to help in

MATH 2600/STAT 2600, Theory of Interest
FALL 2013
Toby Kenney
Midterm Examination
Model Solutions
1. Mr. Almon receives an invoice for $4,000, for payment within 50 days.
He can get a 2% discount if he pays within the rst 10 days. What is the
largest rate

MATH 2600/STAT 2600, Theory of Interest
FALL 2013
Toby Kenney
Homework Sheet 7
Model Solutions
1. Calculate the modied duration and Macauley duration of a 10-year bond
with semi-annual coupons at coupon rate 12%, if it is purchased for a yield
of:
(a) j2

MATH 2600/STAT 2600, Theory of Interest
FALL 2013
Toby Kenney
Homework Sheet 6
Model Solutions
1. The current term structure has the following yields on zero-coupon bonds:
Term(years)
rate
1
2
3%
1
3%
11
2
3.5%
2
4.5%
1
22
5%
3
5.6%
31
2
5.8%
4
6%
How muc

MATH 2600/STAT 2600, Theory of Interest
FALL 2013
Toby Kenney
Homework Sheet 1
Model Solutions
1. Calculate the accumulated value on maturity of the following investments:
(a) $7,000 invested for 20 years at 2% eective annual interest.
The accumulated val

MATH 2600/STAT 2600, Theory of Interest
FALL 2013
Toby Kenney
Homework Sheet 2
Model Solutions
1. Mr. Irving invests $300 a month at j12 = 5% into a fund for his granddaughters education. How much is in the fund when she starts university
8 years 4 months

MATH 2600/STAT 2600, Theory of Interest
FALL 2013
Toby Kenney
Homework Sheet 3
Model Solutions
1. A loan of $15,000 at j12 = 10% is amortised with equal monthly payments
for 2 years.
(a) Calculate the monthly payments.
The monthly payments are given by
15

MATH 2600/STAT 2600, Theory of Interest
FALL 2013
Toby Kenney
Homework Sheet 5
Model Solutions
1. A company are considering a project. The project has the following expected cash ows (all amounts are calculated at the beginning of the year):
Year
Net Cash

MATH 2600/STAT 2600, Theory of Interest
FALL 2013
Toby Kenney
Homework Sheet 4
Model Solutions
1. Calculate the price that should be paid for each of the following bonds to
obtain the desired yield:
(a) Face value $100,000, maturing at par in 10 years, co