1. RATE OF RETURN

2. SIMPLE INTEREST

3. COMPOUND INTEREST

4. MULTIPLE CASH FLOWS

5. ANNUITIES

6. LOAN REPAYMENT SCHEDULES

Financial Math Support Materials

Page 1 of 85

(1) RATE OF RETURN

FINANCIAL MATHEMATICS CONCERNS THE

ANALYSIS

OF

CASH

FLOWS

BETWEEN

PARTIES TO A CONTRACT. IF MONEY IS

BORROWED THERE IS AN INTIAL CASH

INFLOW

TO

THE

BORROWER

BUT

AFTERWARDS THERE WILL BE A CASH

OUTFLOW IN THE FORM OF REPAYMENTS.

A person borrows $100 and promises to repay

the lender $60 after 1 year and $60 after 2 years.

Show the resulting cash flows for the borrower

and lender.

Financial Math Support Materials

Page 2 of 85

Time

Now

1

End of 2 years

Borrower

0

End of 1 year

Lender

2

$100 is loaned out

$120 is received back

The extra $20 is the lenders compensation for

foregoing current consumption to obtain future

consumption.

The lender requires compensation for:

Financial Math Support Materials

Page 3 of 85

THE “TIME VALUE” OF MONEY

CONSIDER A CHOICE OF

$100 NOW, OR

$100 LATER

ANY RATIONAL PERSON WOULD CHOOSE

$100 NOW!

BUT WHY?

“MONEY HAS A TIME VALUE”

Financial Math Support Materials

Page 4 of 85

Time Value of Money (TVM)

Refers to the difference between

The concept enables

Provides the means for valuing multiple cash

flows that occur at different times

The level of interest rates is the index used to

determine prevailing TVM.

Interest rates are determined by the

level of …

For every type of financing transaction there is

potentially a different interest rate.

Interest rates are distinguished by the nature of

the underlying transaction and focus on three

characteristics:

Financial Math Support Materials

Page 5 of 85

An important aspect of valuation is

applying the appropriate interest rate.

For example, valuing a fixed-rate loan to

a highly speculative company using a

government bond rate is inappropriate;

an adjustment must be made reflecting

the relative creditworthiness of the

borrower.

While different TVMs may exist for

every borrower and lender, it is the

Most financial math formulae are a form

of present value calculation; that

is, these formulae identify the future

cash flows of a financial instrument and

then calculate the value at which these

instruments could be exchanged for

cash today.

Financial Math Support Materials

Page 6 of 85

RATE OF RETURN

Suppose I purchase a watch for $200 and sell it a

year later for $250. What is the dollar return and

rate of return of this transaction?

Financial Math Support Materials

Page 7 of 85

Interest

Interest

– a fee for borrowing money

– about as old as civilisation itself

Prime rate

– the interest charged to the largest

and most secure corporations.

Interest is a cost to business, hence it is very

important to understand how it is

calculated and how it impacts on

the business.

There are two basic types of interest

Simple Interest and Compound Interest

Simple Interest

Compound Interest

Financial Math Support Materials

Page 8 of 85

(2) SIMPLE INTEREST

When a financial institution quotes an interest

rate for a loan it can do so in different ways.

For example, a quote 10% p.a. simple interest

has different cash flows than a quote of 10% p.a.

compound interest payable quarterly.

If the quote is offered as a SIMPLE INTEREST

RATE, then the rate is taken as a proportion of

the initial loan amount.

eg 12% p.a. (SIMPLE), is equivalent to

1% per month, or

3% per quarter, or

6% semi-annually.

* NOTE – The quoted rate is often referred to

as the nominal rate.

Financial Math Support Materials

Page 9 of 85

SIMPLE INTEREST

Suppose we lend $300 and quote a simple

interest rate of 8% p.a. What will be the interest

and repayment if the loan is made over:

(a) six months,

(b) one year,

(c) three...