Financial Mathematics by hcj


									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…..
•   To buy your math teacher a large gift
 Where does the money come from?

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

Banks will loan you money….but not for free….
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
• 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
   with in your account?
Our calculations are very similar to the
       simple interest formula.

     We take our starting amount
   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
Start with Interest   the first year

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
       Could we just jump to the
       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

             P (1 + i) n =   A
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,
     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
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