Financial Maths

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FINANCIAL MATHEMATICS

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...
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