Compound Interest Formula - PowerPoint by hqh17862

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									Interest
Interest
Interest
Interest
Interest
Interest
           Asst. Professor D. Urmston
Interest          SUNY Orange

                             Begin
          Learning Objectives
• Understand the concept of compound interest
• Calculate compound interest using a
  spreadsheet
• Compare the results of simple addition, simple
  interest and compound interest for a given
  situation


                                       Continue
     Learning Objectives- The problem
     We want to see the difference compound interest can make when
     someone saves for the future. So imagine you are faced with a choice:

1.    Save your money in a jar ($100/month for 20 years.)(Simple Addition)
2.    Put your money in the bank but then take it out at the end of each year
      and put it in the jar ($100/month for 20 years).(Simple Interest)
3.    Put your savings into the bank as you earn it and earn compound
      interest ($100/month for 20 years- leaving it in the bank).(Compound
      Interest)
      We know that you will have more money under situation 3, but how
      much more?


                                                                 Continue
                                   Main Menu
    How it works: You start with the tutorial and progress through the 3 types of savings. You must
    complete the work for each section before you can move on to the next section. You may skip
     the tutorial if you wish. You may return to the main menu at any time to repeat a section or to
                                       view the learning objectives


             1                                  2                                3




Tutorial- Spreadsheet Basics              Simple Addition                Simple Interest


            4                               5




    Compound Interest                      Quiz                        Learning Objectives
               Tutorial – Menu


How to navigate a   Basic spreadsheet
   spreadsheet            formulas


                                         If the Flash tutorials
                                         are not working, click
                                         here for the alternate
                                         video viewer

Advanced formulas     Copying Formulas


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                Alternate Tutorials

                  Directions: Click on the film reel on the left
                  and a video viewer will open. (It may take a
                  few minutes). Once the video viewer is
                  open, choose File>>> Quick Open File>>>
                  from the drop down menu choose the CD
                  then open the folder Interest
Click Here        Project>>>Tutorials

                    Watch the tutorials in this order:
                    1. Navigation
                    2. Basic_formulas
                    3. Advanced formulas
                    4. Copying1
                    5. Copying2

             When you are done, return to the
             main menu and continue with the
             next section.                                         Main
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Tutorial – Navigation




    How to navigate a
       spreadsheet

  Click to play tutorial. A new window will
   open. When you are finished with the
          tutorial, close the window.


                                              Tutorial
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Tutorial – Basic formulas




        Basic spreadsheet
              formulas

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            tutorial, close the window.


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Tutorial – Advanced Formulas




          Advanced formulas


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              tutorial, close the window.


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Tutorial – Copying formulas




         Copying Formulas


      Click to play tutorial. A new window will
       open. When you are finished with the
              tutorial, close the window.


                                                  Tutorial
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                                                  Main
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          Simple Addition
Welcome to the first step in your journey. All
you have to do to move on is to answer the
question on the following page. Oh, there is
one catch…in order to answer the question,
you need to complete the spreadsheet
assignment on simple addition. Remember,
you are saving $100 per month for 20
years…
                                             Continue


                                              Main
             Click me for the spreadsheet…
                                              Menu
                      Simple Addition
Where is a good place to vacation? Click the location on the map to proceed.




                                                                        Main
                                                        Go back
                                                                        Menu
Sorry, that was incorrect




    Click on the U-turn to try again
                                       Main
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                Correct!



Here is your hint to get to the next section….
76.2% of American households have at least 1
credit card, bank card, or store card.
Hint: you’d better write that number down
somewhere, you’re going to need it! Now go back
to the main menu and complete the next section.

                                          Main
                                          Menu
                  Simple Interest
By now you should have completed the Simple
Addition spreadsheet. If you did then answer the
question below. If you didn’t, then go back and do
it.
What percentage of American households have no credit cards, no bank
cards and no store cards? (Click on the correct answer)

  A. 3%
  B. 23.8%
  C. 13.5%
  D. 42.6%
                                                                   Main
                                                                   Menu
You didn’t write down
that number did you?


       Click Here to Try   Main
            Again!         Menu
       Simple Interest
Now we’re going to see how much
money you would have if you put that
$100 per month into the bank and
cleaned out the bank account at the
end of each year and started over.




         Click here to begin the next
             spreadsheet project
                                        Main
                                        Menu
          Compound Interest-1
   So you want to learn about compound
     interest? First let’s see if you finished
     the section on simple interest
How much more money does a college graduate
earn over a high-school grad?


       50% More $$

       4 times as much $$

       2 times as much $$
                                                        Main
                                              Go Back
                                                        Menu
           Compound Interest-2
Some people are afraid to put their money into a bank,
especially in today’s economy. But banks pay interest so you
can earn more on your savings. Also, your savings are
insured by the Federal Deposit Insurance Company (FDIC) up
to $100,000. So even if your bank goes out of business,
you’ll still get your money. So what if you left the money in
the bank and earned interest for 20 years. How much would
you have then? To find out, we’ll first have to learn about
compound interest…



                                                       Continue

                                                        Main
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       Compound Interest-3

In the last spreadsheet you completed, you simply
added up the interest from each year. But that’s
not how it works in reality. Each year you earn
interest, you add that interest to your principle
and it becomes part of it. So next year, you earn
money on the new principle which includes last
year’s interest. Let’s look at an example…


                                          Continue

                                            Main
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   Compound Interest-4

Let’s say we start with $1,000 which we
put in the bank at an APR of 4%. So at
the end of year 1, you would have
$1,000 x .04 = 40 (that’s the interest)
$1,000 + 40 = $1,040 (that’s your total)

                                      Continue

                                        Main
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   Compound Interest-5

At the end of year 1, you would have
$1,000 + 40 = $1,040
So year 2, you would start with $1040
as your principle and earn interest of
4% on that: $1,040 x .04 = 41.60
$1,040 + 41.60 = $1081.60

                                         Continue

                                          Main
                                          Menu
       Compound Interest-6

At the end of year 2, you would have
$1,040 + 41.60 = $1081.60
Notice that the interest for year 1 was $40 while
the interest for year 2 was $41.60. Year 3, the
interest will be even more because each year the
principle increases as you add the interest from
the previous year.

                                             Continue

                                              Main
                                              Menu
      Compound Interest-7

Now let’s work up a simple spreadsheet that
shows us how this compound interest works.
We will take $500 principle and calculate
compound interest of 6% APR for 5 years.
Click on “Continue” to see a sample
spreadsheet.

                                        Continue

                                         Main
                                         Menu
       Compound Interest-8
Interest rate =            0.06
Year       Principle Interest Ending Balance
Y1           $500.00    $30.00 $530.00
Y2           $530.00    $31.80 $561.80
Y3           $561.80    $33.71 $595.51
Y4           $595.51    $35.73 $631.24
Y5           $631.24    $37.87 $669.11




By now you should be able to create this spreadsheet
without any trouble. So go ahead and try. If you get stuck,
there is help built-in. Remember, you have to submit the
spreadsheet, so you can’t just type in the numbers, you
have to use formulas.



                                                               Continue
                                         Click here to build
                                         your spreadsheet       Main
                                                                Menu
               Compound Interest-9

By now you’ve figured out that compound interest is all about time.
Actually, we refer to compound interest at “the time value of money.”
The spreadsheet you just built was easy, but not very realistic. You see,
most banks compute interest on a monthly basis, using an annual rate.
The math to do this is easy in theory…
You simply take the APR and divide by 12 to get the monthly interest rate.
Example: APR = 10%
.10/12 = .0833 So you would multiply the principle by .0833 each month.
But remember, you need to add the interest each month as well. So let’s
look at what our spreadsheet would look like for our last example…

                                                                 Continue

                                                                  Main
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            Compound Interest-10
         APR=          0.06 Monthly Interest rate= 0.005
         Month   Principle Interest Ending Balance
         M1        $500.00     $2.50     $502.50
         M2        $502.50     $2.51     $505.01
         M3        $505.01     $2.53     $507.54
         M4        $507.54     $2.54     $510.08
         M5        $510.08     $2.55     $512.63
         M6        $512.63     $2.56     $515.19
         M7        $515.19     $2.58     $517.76
         M8        $517.76     $2.59     $520.35
         M9        $520.35     $2.60     $522.96
         M10       $522.96     $2.61     $525.57
         M11       $525.57     $2.63     $528.20
         M12       $528.20     $2.64     $530.84



This is getting to be a pretty big spreadsheet and we’ve only done 1
year’s worth! Now imagine building a spreadsheet to calculate our
original problem of saving $100 per month for 20 years!! There has to
be an easier way…

                                                                  Continue

                                                                    Main
                                                                    Menu
              Compound Interest-11
          APR=          0.06 Monthly Interest rate= 0.005
          Month   Principle Interest Ending Balance
          M1        $500.00     $2.50     $502.50         OR WE COULD JUST DO THIS!
          M2        $502.50     $2.51     $505.01         FV=      $530.84
          M3        $505.01     $2.53     $507.54
          M4        $507.54     $2.54     $510.08
          M5        $510.08     $2.55     $512.63
          M6        $512.63     $2.56     $515.19
          M7        $515.19     $2.58     $517.76
          M8        $517.76     $2.59     $520.35
          M9        $520.35     $2.60     $522.96
          M10       $522.96     $2.61     $525.57
          M11       $525.57     $2.63     $528.20
          M12       $528.20     $2.64     $530.84


Want a faster way to calculate the future value of your investment? Well
we’ve got it. Take a look at the right side of the spreadsheet. Excel has a
formula called FV (future value) and all you have to do is plug in the
variables and have Excel calculate the interest for you.

                                                                                      Continue

                                                                                       Main
                                                                                       Menu
                    Compound Interest-12
                      The FV Formula
      The formula for future value is: FV(rate,nper,pmt,pv,type)
•    Rate is the interest rate per period. Remember to divide by 12 for monthly
     interest.
•    Nper is the total number of payment periods in an annuity. So 12 x #years for
     monthly interest.
•    Pmt is the payment made each period; it cannot change over the life of the
     annuity. If pmt is omitted, you must include the pv argument.
•    Pv is the present value, or the lump-sum amount that a series of future payments
     is worth right now. (Another way to think of this is the money you start with). If pv
     is omitted, it is assumed to be 0 (zero), and you must include the pmt argument.
•    Type is the number 0 or 1 and indicates when payments are due. If type is omitted,
     it is assumed to be 0.
•    Set type equal to 0 if payments are due at the end of the period 1 At the beginning
     of the period. (You can skip this for our purposes).

    Important note: when you enter Pmt or PV you
    must enter them as a negative value, i.e. -100 or                            Continue
    your final answer will show as a negative.
                                                                                  Main
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        Compound Interest-13


Now it’s time to use the FV formula to figure out
 how much money we will have after 20 years.




                                            Continue
                   Click here to
                   complete the              Main
                   spreadsheet               Menu
        Compound Interest-14
So what did you get?
After 20 years of saving $100 per month at 6% APR, you
would have an approximate total of…

       $24,000

       $25,200
       $41,100
       $32,000

                                                 Main
                                      Go Back
                                                 Menu
     Quiz page-1

   APR stands for:

Annual Partial Rate


Actual Percentage Rate

Annual Percentage Rate
                             Next
                            Question
Adjusted Percentage Ratio
                             Main
                             Menu
            Quiz page-2
Bob put $1,000 in the bank for a year.
At the end of the year, he had $1,050
in his account. The $1,000 he started
with is called the:
     Base


     Principal

     Foundation
                                          Next
                                         Question
     Principle
                                          Main
                                          Menu
        Quiz page-3
Bob borrowed $5,000 from the
bank for a year. At the end of
the year, he paid back $5,500.
The $500 he paid is called the:
Bonus


Interest

Penalty
                                   Next
                                  Question
Bribe
                                   Main
                                   Menu
      Quiz page-4
Bob put $5,000 into the bank at an
APR of 6%. The interest was
calculated each month at a rate of
.06/12=.0005 This is an example
of:
Simple Interest


Variable Interest


Reduced Interest
                                      Next
                                     Question
Compound Interest
                                      Main
                                      Menu
        Quiz page-5
Bob put $10,000 into the bank at an
APR of 7%. At the end of the year
he had $10,700 in his account. The
bank must be using:

  Simple Interest


  Variable Interest


  Reduced Interest
                                       Next
                                      Question
  Compound Interest
                                       Main
                                       Menu
       Quiz page-6
Bob put $10,000 into the bank
at an APR of 8%. The bank
uses simple interest. At the
end of the year Bob will have:
  $10,080


  $10,800


  $10,000
                                  Next
                                 Question
  It depends on current
                                  Main
  interest rates.                 Menu
        Quiz page-7
The FDIC makes sure your
money is safe when you put it
into a bank. FDIC stands for:
  Federal Deposit
  Insurance Capital
  First Deposit Is
  Covered
  Federal Deposit Insurance
  Corporation                    Next
                                Question
  First Definitive
                                 Main
  Interest Charge                Menu
         Quiz page-8
In the FV(rate,nper,pmt,pv,type)
formula that we used in Excel,
“pmt” represents:
  The payment you make each month
  into your savings account.

  The payment you get each
  month from the interest
  earned.
  The payment you get at a
  future date.
                                      Next
                                     Question
  The amount you start with before
  you begin saving each month.        Main
                                      Menu
         Quiz page-9
In the FV(rate,nper,pmt,pv,type)
formula that we used in Excel, if the
APR was 12%, the “rate” would be:

   6%


   12%


   1%
                                    Next
                                   Question
   3%
                                    Main
                                    Menu
         Quiz page-10
In the FV(rate,nper,pmt,pv,type)
formula that we used in Excel, if you
were saving money for 10 years, the
“nper” would be:
   10


   12


   100
                                    Next>
   120
                                    Main
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 Sorry, that’s incorrect




Go back and try again.


                           Main
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    Correct!




Click here, then go on to the
       next question!
                                Main
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               You’re done!


   So, by simply adding up your $100 per month,
   you would save $24,000 over 20 years. If you
   put that same money in the bank at an APR of
   5%, you would end up with over $41,000
   thanks to compound interest!
If you haven’t completed the quiz, go back to the
   main menu and give it a try!
                                            Main
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        You’re done!



So, how did you do on the quiz?




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