Perpetuities (section 4.3)
A perpetuity is an annuity where the
payments begin on a fixed date and
continue forever
since payments continue forever, it is
meaningless to calculate accumulated
values
we will only look at the present value
of perpetuities

Chapter 3 Simple Annuities
Introduction
Suppose you deposit $500 every 6-months
for 2-years.
How much will you have accumulated
immediately after the 4th deposit if j2 = 6%?
0
500
1
500
2
500
3
500
4
S
i = 0.06/2 = 0.03
S = 500 + 500(1.03) + 500(1.03)2 +

Discounted Value of An Ordinary Simple
Annuity (section 3.3)
Consider the following
An ordinary simple annuity consisting of
n-payments of $1
we wish to determine the present value, A,
of these payments at the beginning of the
term
that is, what is the

Chapter 4 General and Other Annuities
General Annuities (section 4.1)
General annuities are annuities (either
ordinary or due) where the interest period
and the payment period are NOT the same
1.Semi-annual payments, quarterly interest
2.Monthly payments,

Other Simple Annuities (section 3.4)
(I) Annuity Due
An annuity-due is an annuity where the
periodic payments are due at the beginning
of each payment interval
term of an annuity-due starts at the time of
the 1st payment and ends one period after
the dat

Annuities Where Payments Vary
(section 4.4)
Not all annuities have a level series of
payments; instead we are going to look at
annuities where the payments change every
period
Two Standard Types
(I)
Payments vary in terms of a constant
ratio
these are an

Compound Interest at Changing Interest
Rates (section 2.7)
In all examples/exercises so far, the interest
rate was assumed to be constant throughout
the term of the investment
frequently, however, the interest rate
changes over the term of a loan or
inve

Determining the Rate and Time (2.5)
(I)
Determining the Rate
Given: P, S, n
Determine: i
Start with: S = P(1 + i )n
(1+ i )n = S/P
(1+ i ) = (S/P)1/n
i = (S/P)1/n 1
most of the time, you are asked to solve for
jm = mi
Example 2.5.1
At what nominal rate j2

Determining the Term of an Annuity
(section 3.5)
Given: S or A, R, i
Determine: n
Method
You can use logs to solve:
S=R
s n |i
or
A=R
an |i
Problem
n will rarely be an integer
will need to calculate a final payment that
is different from R in order to h

Chapter 2 Compound Interest
Fundamental Compound Interest Formula
(section 2.1)
Compound Interest
The interest earned in any given period of
time is added to the principal and it
thereafter earns interest
the interest is said to be compounded
and your in

Chapter 8 - Fixed Income Investments
Introduction (section 8.1)
Key Points
1. A fixed income security, FIS, (fixed
income investment) is an investment
where a lump sum of money is invested
and an income stream is returned
the cash flows of the income str

Types of Risk (sections 8.2 and 8.3)
The yield rate (market interest rate) on an
investment will depend on the risk
associated with the investment
For Example
Two different corporations may issue bonds
on the same day, with the same values of F,
C, n and

Chapter 7 Business Decisions, Capital
Budgeting and Depreciation
Net Present Value (section 7.1)
Businesses are frequently faced with the
problem of deciding whether an investment
or business venture should be undertaken
in many situations, alternative p

Chapter 1 Simple Interest and Discount
Simple Interest (section 1.1)
In any financial transaction, there are two
parties:
The lender and the borrower
If you deposit money into a bank account,
you are lending money to the bank
Consider the following transa