Principal                       $100.00
           Interest                         5.00%
           Time(Years)     Annual Interest Rate    Initial Investment    Interest Earned
           Year 1                           5.00%                $100.00             $5.00
           Year 2                           5.00%                $105.00             $5.25
           Year 3                           5.00%                $110.25             $5.51
           Year 4                           5.00%                $115.76             $5.79
           Year 5                           5.00%                $121.55             $6.08
            Pn =  value at the end of so many periods
            pv = present value or beginning value
            r = interest rate (constant in this case)
            n = number of periods
            For our case, we have Pn = 100*(1+.05)^5
            If you type  = 100*(1+.05)^5 into a column and press enter, it will give the 
            answer $127.63 which is what we calculated above. 
            The last one was simple interest and we didn't calculate interest on let's say 
            a bank account. With compound interest we are going to account for every 
            year in the total amount.
            So let's say we put an initial amount of  $100.00 in our bank account. After 
            year 1 with 5% interest, we will have $105.00. Now, with compound 
            interest, $105.00 is our new beginning amount for year 2. We must 
            multiply (105)(0.05) to get our interest payment. Thus, our total will be 
            105 + (105)(.05) = 105 + 5.25 = 110.25 dollars. For the third year, our 
            beginning amount will be $110.25 with an interest rate of 5%. Thus our 
            total after year 3 will be $110.25 + (110.25)(.05) = $110.25 + $5.51 = 
            $115.76.
         Formula
         Pn = pv*(1+r)^n
                                    140
         Account Value
                   $105.00
                   $110.25
                   $115.76          120
                   $121.55
                   $127.63
                                    100
Pn =  value at the end of so many periods
pv = present value or beginning value
r = interest rate (constant in this case)80                                                                      Annual Interest Rate
n = number of periods
                                                                                                                 Initial Investment
For our case, we have Pn = 100*(1+.05)^5                                                                         Interest Earned
If you type  = 100*(1+.05)^5 into a column and press enter, it will give the 60                                  Account Value
answer $127.63 which is what we calculated above. 
The last one was simple interest and we didn't calculate interest on let's say 40
a bank account. With compound interest we are going to account for every 
year in the total amount.
                                      20
So let's say we put an initial amount of  $100.00 in our bank account. After 
year 1 with 5% interest, we will have $105.00. Now, with compound 
interest, $105.00 is our new beginning amount for year 2. We must 0
multiply (105)(0.05) to get our interest payment. Thus, our total will be Year 1Year 2Year 3Year 4 Year 5
105 + (105)(.05) = 105 + 5.25 = 110.25 dollars. For the third year, our 
beginning amount will be $110.25 with an interest rate of 5%. Thus our 
total after year 3 will be $110.25 + (110.25)(.05) = $110.25 + $5.51 = 
$115.76.
140
120
100
80                                          Annual Interest Rate
                                            Initial Investment
                                            Interest Earned
60                                          Account Value
40
20
0
Year 1Year 2Year 3Year 4     Year 5