Yellow
1. Find the present value of an annuity which pays $2,500 at the end of each year for 30
years. Assume an effective annual interest rate of 9%.
2. A perpetuity pays $5,000 every year. The effective annual interest rate is 8.5%.
Find the present val
1. Calculate the nominal annual rate of discount convertible semi-annually that is equivalent to a
nominal annual rate of interest of 10%(9%) per year convertible monthly.
Solution:
with
2. A $15,000 loan is repaid with one payment of $18,375.65 after 36
Practice for midterm exam
,
1.
If the effective rate of interest on an investment is 6%, what is the nominal rate of
interest compounded monthly?
2. Calculate the nominal annual rate of discount convertible semi-annually at which you
can double your money
Chapter 3: Basic Annuities
Chapter 3: Basic Annuities
Please read Ch 3.1 to 3.8 from The Theory of Interest.
2 important notes:
1. occurs one payment period BEFORE the 1st payment
3.1
Introduction
Time 0
1
Value
X
like a
loan
2. ends on the date of the la
Ch 4: More General Annuities
Please read Ch 4.1 to 4.9 from the Theory of Interest.
Ch 4: More General Annuities
Example:
Given i(4) on an annuity with annual payments. Find j (ie. the effective
annual rate).
4.1 Introduction
in Chapter 3, annuities were
University of Alberta
Department of Mathematical and Statistical Sciences
MATH 253 (A1)
Theory of Interest (Financial Mathematics)
Fall 2016
Instructor: Dr. Hafizah Yahya
Office:
CAB 471
E-mail:
hafizah@ualberta.ca
Office Hours: After class by appointment
Math 253 Practice Midterm I
Last Name: _
First Name: _
STUDENT ID: _
Instructions:
1)
2)
3)
4)
5)
6)
7)
8)
Please put your one card on your desk.
The exam is closed book and no formula sheets are allowed.
No communications with other students are allowed.
Math 253 Practice Midterm II
Last Name: _
First Name: _
STUDENT ID: _
Instructions:
1)
2)
3)
4)
5)
6)
7)
8)
Please put your one card on your desk.
The exam is closed book and no formula sheets are allowed.
No communications with other students are allowed
Math 253 Practice Midterm II
Last Name: _
First Name: _
STUDENT ID: _
Instructions:
1)
2)
3)
4)
5)
6)
7)
8)
Please put your one card on your desk.
The exam is closed book and no formula sheets are allowed.
No communications with other students are allowed
Chapter 6: Financial Instruments
Please read Ch 6.1 to 6.4, 6.10 from the Theory of Interest.
6.1
Introduction
- interest theory can be used to evaluate the prices of values of bonds
and equity (common stock, preferred stock)
- this chapter will show how
Ch 5: Amortization Schedules and Sinking Funds
Please read Ch 5.1 to 5.6 from the Theory of Interest.
5.1 Introduction
there are two methods for paying off a loan:
(i) Amortization Method - borrower makes installment payments at
periodic intervals
(ii) S
Ch 4: More General Annuities
Please read Ch 4.1 to 4.9 from the Theory of Interest.
4.1
Introduction
in Chapter 3, annuities were described as having level payments
payable at the same frequency as what the interest rate was being
converted at
in this c
Chapter 1 Part 2
Chapter 1 Part 2
1.4 Simple Interest
Example:
Example of Simple Interest:
Andy deposits $1000 into a bank. The account pays simple
The simplest example of interest is a loan agreement two children
interest of 8% per year. Calculate the ac
Chapter 6: Financial Instruments
Please read Ch 6.1 to 6.4, 6.10 from the Theory of Interest.
Chapter 6: Financial Instruments
o accumulation bonds or zero-coupon bonds: bonds without
coupons and pay out a lump sum in the future.
o a mortgage bond: a bond
Math 253 SOA Practice Problems Solution
(Covers Ch 1 and 2)
1) Answer: D
There are only two real possibilities:
Two consecutive 3 year CDs: 10,0001
12
0.05
0.05
1
4
4
12
20
13,473.51
4
0.0565 0.04
One 5 year CD and a 1 year CD: 10,0001
1
13,
Math 253 SOA Practice Problems
(Covers Ch 1 and 2)
The following problems are taken out from previous SOA exams:
The solutions to these questions will be posted shortly.
1) A bank offers the following choices for certificates of deposit:
Term
(in years)
1
Ex. 6.3 A bond pays semiannual coupons at an annual rate of
10% of the nominal value. The annual effective yield-to-maturity is
currently 4% and the price paid per $1,000 par value is $1,404.06.
If the bond is redeemed after 7 years, calculate the redempt
1.9 Force of Interest and discount (Omit force of discount)
Recall: an annual compound interest is the change in the account value over one year, expressed
as a percentage of the value at the beginning of the year.
We now consider the case of interest tha
1.5 Compound Interest
Under simple interest, the interest is not reinvested to earn
additional interest.
The theory of compound interest handles this problem by
assuming that the interest earned is automatically reinvested.
With compound interest the tota
2016-11-04
Chapter 5: Amortization Schedules and Sinking
Funds
5.1 Introduction
There are two methods for paying off a loan:
(i) Amortization Method - borrower makes series of
payments at periodic intervals
(ii) Sinking Fund Method - borrower makes paymen
Chapter 3 Basic Annuities
3.1 An annuity is defined as a series of payments,
usually of equal size, made at periodic(equal) time
intervals.
payment period - length of time between
successive payments
term of an annuity - length of time from the
beginnin
Interest: compensation that a borrower of money pays to a lender for its use
Principal: initial amount of money invested
Accumulated value: total amount of money the borrower pays to the lender after a
period of time
Interest = Accumulated value Principal
1.8 Nominal Rate of Interest and Discount Convertible
Definition
An effective rate of interest (discount) is paid once per year at the end (beginning) of the year
A nominal rate of interest (discount) is paid more frequently during the year (m times) and
Math 253 Practice Midterm I
Last Name: _
First Name: _
STUDENT ID: _
1)
2)
3)
4)
5)
6)
Please put your one card on your desk.
The exam is closed book and no formula sheets are allowed.
No communications with other students are allowed.
You are permitted t
Chapter 6 Bond Valuation
We will use interest theory to evaluate the prices and
values of bonds given a yield rate,
how a bond is amortized and determine the value of a
bond on a given date after it has been purchased.
Government issued bonds are called
5.6 Loans:The Sinking Fund Method is a method
of paying off a loan in which a borrower pays
interest payments throughout the loan period and
then pays the loan in full at the end of the loan
period. The interest payments are called service
payments.
The l
1. A loan is being repaid with 25 annual payments of 300 each. With the
10th payment, the borrower pays an extra 1000, and then repays the
balance over 10 years with a revised annual payment. The effective rate
of interest is 8%. Calculate the amount of t
Chapter 1: Measurement of Interest
Interest Earned during the nth period:
Please read Ch 1.1 to 1.10 from The Theory of Interest.
In = A(n) A(n 1)
- interest earned is the difference between the Accumulated Value
1.1 Interest
at the end of a period and th
Ch 5: Amortization Schedules and Sinking Funds
Ch 5: Amortization Schedules and Sinking Funds
Please read Ch 5.1 to 5.6 from the Theory of Interest.
Retrospective Method
calculates outstanding loan balance by looking into the past
Let P be the level rep
University of Alberta
Math 253 (Q1)
Solution Midterm Examination(white)
1. (3 marks) If the effective rate of interest on an investment is 7%, what is the nominal rate
of interest compounded quarterly?
2. (2 marks) You invest $1000 now, at an annual simpl
Ex. Determine the PV at time 0 of payments of $5 at time 1 year, $10 at time 2
years, $15 at time 3 year,and so on, assuming an annual effective interest rate of
5%.
Ex. Determine the PV at time 0 of payments of $75 at time 0, $80 at time 1 year,
$85 at t
11/30/2016
Amortization of Premium and discount
Book Value of a bond tells the value of a bond on the yield at
which it is purchased, so it does not change in response to
changes in the market yield that occur after the bond is purchased.
= book value or
2016-11-02
5.1 Introduction
there are two methods for paying off a loan
Amortization Method
Borrower makes installment payments at
periodic intervals
Sinking Fund Method
Borrower makes installment payments as the
interest comes due and pays back the orig
Decreasing annuity-immediate:
payments of n, n - 1, n - 2, . . . , 1 are made at the end of the
1st, 2nd, 3rd, . . . , nth period, respectively, with periodic interest rate i.
The present value of a decreasing annuity-immediate is denoted by
( )
(
)
)(
(
08/02/2016
Annuity-Immediate and AnnuityDue
Annuity-Immediate: payments at the end of
each period
Annuity-Due: payments at the beginning of
each period
The accumulated value of a series of
payments is the sum of accumulated values
of each payment.
The