# Compound Interest Formula - PowerPoint by hqh17862

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

Begin
Learning Objectives
• Understand the concept of compound interest
• Calculate compound interest using a
• 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
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

4                               5

Compound Interest                      Quiz                        Learning Objectives

How to navigate a   Basic spreadsheet

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

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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

Watch the tutorials in this order:
2. Basic_formulas
4. Copying1
5. Copying2

main menu and continue with the
next section.                                         Main

How to navigate a

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

formulas

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open. When you are finished with the
tutorial, close the window.

Tutorial
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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 – 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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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
you are saving \$100 per month for 20
years…
Continue

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Where is a good place to vacation? Click the location on the map to proceed.

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Go back
Sorry, that was incorrect

Click on the U-turn to try again
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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.

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Simple Interest
By now you should have completed the Simple
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%
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You didn’t write down
that number did you?

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.

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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

50% More \$\$

4 times as much \$\$

2 times as much \$\$
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Go Back
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
insured by the Federal Deposit Insurance Company (FDIC) up
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

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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
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

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Compound Interest-4

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

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Compound Interest-5

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

Continue

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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

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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

Continue

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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
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

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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

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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

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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
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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
complete the              Main
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

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Go Back
Quiz page-1

APR stands for:

Annual Partial Rate

Actual Percentage Rate

Annual Percentage Rate
Next
Question
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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
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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
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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
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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
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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
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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
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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

The payment you get each
month from the interest
earned.
The payment you get at a
future date.
Next
Question
you begin saving each month.        Main
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%
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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
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Sorry, that’s incorrect

Go back and try again.

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Correct!

next question!
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You’re done!

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!
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You’re done!

So, how did you do on the quiz?

Take quiz   Main