Partial Payments (section 1.4)
When a person borrows money, they can
pay back the loan, with interest, in one of
two ways:
1. With a single payment on the due date
2. With a series of partial payments
during the whole term of the loan
Methods to Handle Pa

Introduction to risk management
Producer-commodity market-buyer
For the producer, the risk commodity
makes its profit move positively with the
price of the commodity in the market,
hence, it called an inherent long position
For the buyer, a risk commodity

Make-to-market: margin updated daily,
the difference between the buyer and
seller will be report daily based on the
underlying asset price change; there are
initial margin (10% of the notional price),
maintenance margin, and margin call
If the margin belo

Strangle: can reduce premium, ie 3545 strike call and put, also increase the
stock price move required to have a
profit
Exercise: 3.11 collar. 3.13 straddle.
3.15 ratio spread
Summary:
Straddle: buy call and put at the same
strike price (premium=total pre

Future contract
More obligations as traded at the
exchange or clear housing
Less credit risk, more liquid, but harder
to the customizations
Differ from option: option is the right to
buy and sell, future is the obligation
Make-to-market: margin updated
da

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
Example 2.5.1
At what effective rate j2 will $5000 earn $1800
of interest over 6 years? Ho

Chapter 3 Simple Annuities
Definitions
Introduction
1.
An annuity is a sequence of periodic payments,
usually equal, made at equal intervals of time
2.
The payment interval is the time between
successive payments
3.
The term of an annuity is the time from

Determining the Rate and Time (2.5)
(I)
Determining the Rate
Given: P, S, n
Determine: i
Start with:
Example 2.5.4
If you invest $1000 today, how much money do you think
you will have in 5-years time? In a recent CNN survey of
Americans, the median answer

Other Simple Annuities (section 3.4)
(I) Annuity Due
Note
If the periodic payment is $R, then
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
p

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
S = P(1 + i

Chapter 1 Simple Interest and Discount
Simple Interest (section 1.1)
In any financial transaction, there are two
parties:
Interest is calculated on the original principal
only during the whole term of the investment
(or loan), at the stated annual rate of

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 inves

Determining the Term of an Annuity
(section 3.5)
Given: S or A, R, i
A couple wishes to accumulate $10,000 by depositing
$700 at the end of each quarter in a fund earning j4 = 6%.
How many deposits must they make and what is the size
of the final deposit

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
Definition

Chapter 1 Simple Interest and Discount
Simple Interest (section 1.1)
In any financial transaction, there are
two parties:
The lender and the borrower
Consider the following transaction:
Person A lends money to person B
person A is called the lender or
in

Exercise style: governs the times at which
exercise can occur.
European-style option: exercise can
only occur at expiration
American-style option: exercise at any
time during the life of the option
Bermudan-style option: exercise during
a specified period

Callable Bonds (section 6.4)
In General For bonds callable at par
Callable bonds are bonds that a bond issuer can pay
back before the redemption date
1
If i < r (bond sells at a premium), use the
earliest possible call date in your price
calculations
bon

Price of a Bond Between Bond Interest Dates (section
6.5)
So far we have been calculating the price of a bond
assuming the bond was purchased on a bond coupon
date
(Or purchased on the date of issue, which is one
period before the first coupon is due)
in

Determining the Yield Rate (section 6.6)
So far, we have been calculating the price of a bond
in situations where the yield rate has been given
Example 6.6.2
A $1000 bond is due in 10 years. It is redeemable at 98
and pays interest at j2 = 9%. It is quote

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
Thus,
If the interest rate does not change
2.
The origin

Chapter 6 Bonds
Introduction (section 6.1)
When a corporation or government needs a large sum
of money for a long period of time, they can issue
bonds
the bonds can be sold to a large number of
investors
A bond is a written contract between the issuer
(bo

Chapter 10 Life Annuities
Review Interest Only Annuities
(section 10.1)
1.
Accumulating/Discounting Single Sums
S = a.v. of a single sum of money
A = p.v. of a single sum of money
S = A (1 + i )n
A = S (1 + i )n
(i)
(ii)
New notation
v = (1 + i )1 =
2.
In

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 5 Repaying a Debt
How the Above Table Works
Amortization of a Debt (section 5.1)
1.
Ik = i (Bk1)
Interest bearing loans are often paid back by means
of a series of equal payments at equal time intervals
we say the loan is being amortized
2.
Pk =