# Financial Mathematics by hcj

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```									The Study of Money
Simple Interest
For most of your financial plans,
throughout your life, there will be
two groups involved.
The Bank         The Individual
There will be times when you find
yourself in a situation where you
need more money than you have…

•   To purchase a house
•   To purchase a car
•   To get married
•   To purchase furniture, a stereo, a special trip…..
Where does the money come from?

Typically, people will go
to a bank for a loan.

Interest is the fee charged
for the use of money.

• Interest can be calculated
two different ways:

• simple or compound.
For simple interest,
the bank charges you a certain
percentage of the loan amount.
• Simple Interest is calculated using:

I = Prt

I = Interest (cost of the loan)

P = Principle (amount of the loan)

r = rate (interest rate, as a decimal)

t = time (in years)
You go on a trip to the Caribbean with your
friends for March Break.
It is all inclusive, at a cost of \$1800.00, and
you pay with your new credit card.

Your CC charges 19% interest per year,
I = Prt
P = 1800, r = 0.19, t = 1/12
I = 1800(0.19)(1/12)
= \$28.50
So, you would owe the bank \$1800.00, plus \$28.50 interest.

Suppose you paid \$200.00 off the debt. That means for the next month,
they would use \$1628.50 for the calculation.

You would pay interest to the CC company until you paid the entire debt.
• As with any equation, as long as you
are given three of the variables, you
can solve for the fourth….
Complete the given
worksheets on
simple interest
before we move
in to compound
interest.
• While simple interest offers a good
initial illustration, most of your
dealings with the bank will involve
another kind of interest calculation
• Compound Interest
Compound Interest
Since our first example involved you
going into debt, let’s look at an example
where you will be earning money.

Examine the situation below:
Suppose you deposited
\$1000.00 into an account.

You can get 6% interest for 4 years.

How much will you end up
Our calculations are very similar to the
simple interest formula.

We take our starting amount
(\$1000.00),
and multiply by our interest rate
(6% as a decimal = 0.06)
Note: Because after each year you want
to know how much in total is in your
account, not just the interest, we add a
“1” to the calculation.

So for 6% interest, we multiply by
“1” plus 0.6, which equals1.06
Amount in the bank after

1000(1.06) = 1060.00
Now Start Interest    Amount in the bank after
with                  the second year

1060(1.06) = 1123.60

And so on!
• As a short cut:, we can do all the multiplications
in one step

1000(1.06)(1.06)(1.06)(1.06) = 1262.48

These can be compressed into a power! so…

1000(1.06)4 = 1262.48
final stage given just the
initial values? YES!
Suppose you deposited \$1000.00
into a savings account. If you
could get 6% for 4 years, how
much would you end up with?

1000(1.06)4 = \$1262.48
Replace
the

P (1 + i) n =   A
numbers
with
variables
Amount formula for compound interest
A = P(1 + i)n

A = Final Amount
P = Starting Principle
i = interest rate per cycle (always
in decimals)
n = number of cycles (months,
years…
Invest \$1000.00
at 4.25%
for 7 years.

How much will you have?
A = P(1 + i)n
• A = 1000(1 + 0.0425)7
•    = 1000(1.0425)7
•    = \$1338.24
Stop Here Today

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