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Chapter 6

The Science of Financial Numbers

The origins of finance is attributed to the need of holding value, the humble early

development can be traced back to blacksmiths. Today banking systems has become quite

sophisticated. Banks are also a business like any other whose aim is not just providing a

service but to derive a profit from rendering these services. Like all businesses within the

same business banks also compete against each other for the best cut in the market. Some

banks will combine forces in order to gain the majority client base within the market. The

Amalgamated Banks of South Africa adopted from nature the strength in large numbers

concept. This is a perfect example of how there is security and strength within these

numbers. ABSA is the amalgamation of four banks originally United, Alied, Turstbank and

Volkskas. With this amalgamation came a well planned organisational restructuring as well

as the shifting of some focuses a dynamic value and mission statement was adopted,

processes and programs are constantly under review and being redesigned.

Sometimes things do not go according to the plan, not even financial statements canforewarn about any possibility of the business falling apart in a few months.

All banks should keep a cash ratio, as laid down by the reserve bank, which must be held

back when the bank receive a deposit from customers, it the cash ratio is, r=15(20%) it

means that a bank excepting a deposit of 100 can only lend out 80% in this case 80 and

must retain the 20, there is a multiple factor involved with this process. Since the bank are

repaid the 80 which includes monthly interest on loan repayments. A deposit of a 1000

allows the bank to lend out 80% in this case 800, we assume after calculation that

repayments will be 100 per month, the bank can thus retain 20% and in this case lend to

customers 80% this results in hundreds becoming thousands.

Should banks fail to comply with this ratio the results can be disastrous. This is what

happened and contributed to the destruction and collapse of Saambou Bank that used to

trade in South Africa.

It all probably started with a rumour, originated from an unhappy customer or a very powerful

investor, and even could have been bad management of funds or the wrong business

decision, but whatever the reason that led to the cash withdrawals frenzy of investors, that in

turn resulted in the cash ratio to drop below the reserve banks requirements, happened in

almost a blink of an eye. Usually banks will rectify minor cash ratio problems by either

borrowing from the reserve bank or borrowing from the government. But Saambou could not

do either of this they had no credit left, and there was only one way for the financial

institution to go and that was to be bought, or rather in this case the debt to be taken over,

since hardly any assets had remained. The event occurring or the possibility of that eventtaking place could not be predicted beforehand nor the chance of it since the human nature

is far more complex than we believe and Saambou are an perfect example of just how

volatile a business can be.

Banks derives income from investment payouts in relation to loan repayments. That explains

the difference on interest rate percentages between loans and investments. At the turn of the

21 century income also became derived from charges levied on services rendered, charges

increasing at a phenomenal rate. There were certain areas of abuse on the banks side and

they took advantage of the situation by overcharging their customers and service standards

were unacceptable. Organisations came into existence to protect customers should they be

treated unfairly. The problem is that the public are in the dark in how these charges are

decided upon and have led to many disputes, between clients and the bank. Banking

systems and security programs, etcetera, cost the banks billions. The aim is to protect the

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money it holds and customers personal details, Overall cost and pricing within any market

are also linked to inflationary factors, and the changes in an economy local and international.

There is not just one aspect but many numbers that influence prices and interest rates for

that matter. Interest rates are influenced by the reserve banks lending rate and the position

of foreign exchange markets, which is directly linked to trade.

Money deposited into a bank account, earns interest at a certain percentage each year.Interest can be calculated in two basic ways, simple and compounded. Simple interest is

earned on initial capital only, and is withdrawn from the account as soon as it is earned. Only

the capital is left to continue earning interest.

Interests that are earned on the sum of the capital including interest previously earned are

compounded interest. Each interest allocation is left on the account including the capital, we

can say that inters are earned on interest and interest are also earned on the capital.

The calculation of simple interest is one of the least complicated problems of financial

mathematics.

A certain amount of money is deposited into a bank account and a certain rate of interest is

allocated against it. At the end of a specific period of time the capital would have increased

by a certain fraction of its capital value.

The equation is very logical in determining the total interest that was earned after the

specified period of time has lapsed.

IfC is the symbol for Capital, i for interest and n stands for the period of time, the relation

between these characters will result in answer L which is the total amount of interest that

was earned.

C x n x i=L

If we invest 1000 for 3 years at 6% then capital C =1000, time n 3 years and interest i 6 %

the result will be 180.

1000 x 3 x 6%=180

Simple interest calculation is based on the assumption that the interest is not reinvested at

the end of each year.

Compounded interest looks exactly the same in the first year, compared to Simple interest

calculation but that is where the relationship ends.

Capital is invested in such a manner that interest is received on the capital as well as on the

initially earned interest.

The capital increases more quickly than simple interest, as a result of that the account earns

interest on its already earned interest, the value of the sum of the interest and the capital.We can look at this in stages.

The first year interest calculation is as follow:

C x n x i=L

Time n in this case is no longer 3 years but remain for the exercise 1 which equals 12

months.

1000 x 1 x 6%=60

The second year interest that was earned the previous term is included within the capital,and interest is calculated on this amount.

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1060 x 1 x 6%=63,60

Interest earned at the end of the third year is 67, 42 the capital will now have grown to the

amount of 1, 250.42.

The simple interest calculation only earned 180 and the compounded interest yielded 250,42 for the same period of time.

The benefit of compounded interest is that the capital increased in value over time, which is

not the case of simple interest.

Frequently compounded interest, where interest are calculated for argument sake quarterly,

has the advantage that interest are more frequented and since it is compounded more

frequently it means that more interest is earned, although there is not an immense

advantage. The maximum capital will never be greater than that which is given by the

formula. ni

M=Ce

M refers to the maximum amount of capital C is the initial capital and e refers to the base ofthe natural logarithms (2,718) and n is the time in years and fractions of years, i remains the

rate of interest.

Actual investment conditions are more complex and the fluctuation in interest rates (caused

by variable factors and market conditions) results in recalculation, adjustments and are also

influenced by the fact that there are frequently a value of capital below which interest is not

paid.

When a creditor transfers a sum of money to a debtor are known as a loan. Loan

amortization is based upon an agreement that after a period of time this loaned sum of

money, including any and all interest that was accrued, will be paid back in full, either as

instalments or at the end of the term.An amortization plan must thus allow for repayments of capital and interest accrued, so that

at the end of the agreed term both the debt and the interest are liquidated.

Interest rates can be fixed or directly related to changes within the market. Normally at the

end of each month a part of the actual loaned amount including interest is paid onto the loan

account, and as the balance due on the account decreases thus the amount due on the loan

also decrease.

Before the turn of the 21 century banks used to offset interest paid on loans which were an

income for the bank against interest that was paid out and seen as an expense for the bank.

In this case are purely based on money value. There is a fascinating aspect to finance.

Finance is a perfect example of applied scientific discipline, mathematics.

In every organisation the motive for its sole existence is to provide services or goods tocustomers and do so at a profit. Accounting made it possible for a business to apply

mathematics in such a format, precise calculations can be done on income, profit and loss.