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Interest and Saving Money

1.  Simple Interest - interest earned just one time, calculated just one time
        Formula  =>    Interest = Principal x Rate x Time                                     

                                            I   =  P   *    R    *     T

                            money earned = $ in bank times percent times number of years

        Example #1:  $5,000 at 6% for 30 years.  Take 5,000 x 0.06 x 30 = $9,000 in interest.

        Example #2:  $700 at 5.5% for 18 months.  

                            Take 700 x 0.055 x 18/12 =  $57.75  (you must convert months to years,
                                    so you take 18 divided by 12)

2Compound Interest - interest earned upon previous interest

        Formula  =>   Amount = Principal * (1 + i/n) ^ nt

          P = Principal ($), i = rate (as a decimal), n = number of times the money is compounded in a year (like daily), and t = number of years.  You need to do all the operations inside the parentheses first.   You raise that quantity to the  nt  (n times t) power.   The last step is to multiply by the principal.

        For instance, $400 deposited at 5%  and left for 40 years, compounded daily.  What is the total?

        A = 400 * (1 + 0.05/365 ) ^ (365 * 40)   which gives $2,955.22.  That means $400 turns into about $3,000 after 40 years if the percent is 5%.  The $400 is a one time deposit and then it is left alone.

        A good question that comes up is:  How much money is necessary at 6% for 50 years to become one million dollars ($1,000,000), compounded monthly?

    (calculate your answer first and then scroll down)

   1,000,000 =  P * ( 1 + 0.06 / 12) ^ (12 * 50)

   1,000,000 =  P * ( 1 + 0.005) ^ 600

   1,000,000 =  P *  (1.005) ^ 600

    1,000,000 = P * (19.93595542)

    1,000,000 / 19.93595542 = P

     $50,160.63 = P       

     This means that if you could deposit $50,000 right now as a 7th grader, fifty years later you would be a millionaire (at 6% and not taking any money out).  You would not have to add any money to this account.  If the interest rate is better than 6%, then you won't need as much money.

3.  The power of money - rule of 72

        The rule of 72 is a useful tool to estimate how much money your savings will turn into after leaving it in the bank after a period of time.

        Take the number 72 and divide it by the percentage (don't turn it to a decimal).  The answer will be the number of years it takes your money to double.

        For instance, if you get 9% at a bank, then 72 / 9 means that it will take 8 years to double your money.   If you get 12%, then 72 / 12 means 6 years to double.

    Let's put $1,000 into two banks, one at 6% (12 year cycle) and 12% (6 year cycle).  We'll start with the year 2000.

                            Bank A                                 Bank B

year 2000          $1,000                                   $1,000
year 2006                                                        $2,000
year 2012           $2,000                                 $4,000
year 2018                                                       $8,000
year 2024           $4,000                               $16,000
year 2030                                                     $32,000
year 2036           $8,000                               $64,000

   Any questions?  Do you see why people like to put their money into the stock market, which might make them more than 12%?   Can you imagine what can happen to your money if you earn 20% per year like Warren Buffet?

  What's the point of this section on the rule of 72?  Get the best interest rate you can because over time the results can be very significant! 

    P.S.  Anyone know why we use 72?  and not 54 or 91?

4.  Annuities -  Annuities are regular deposits of money into an account, like depositing $10 every paycheck.
        Formula =>  Principal * ((1 + R/1200) ^ (12 * T) - 1) / (R/1200)

        If a 7th grade student regularly saves money, how much money would accumulate?

        $0.50 a day (not buying one can of soda )   at 6%   for 52 years (until retirement)                 gives a total of $60,118.82!!

        $0.85 a day (not buying a 20 ounce bottle)   at 6% for 52 years (until retirement)
                gives a total of $109,502.14 !!

        $30 a month (not buying cable TV)  at 6%  for  44 years (age 21 until age 65)
               gives a total of $77,527.96!!

        $2 a day (not buying a pack of cigarettes a day) at 6% for 44 years (age 21 until 65)
               gives a total of $155,055.91!!

    Thus, the key to saving money is NOT buying things and saving the money in a bank instead;  not getting a better job and making more money.

(updated 9-23-99)

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