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Compounding Interest

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					The Present Value of $1

   10% annual compounding,                   4 years

Present     Future Single            times                  Factor
Value =       Amount                                   I = 10%, n = 4

   ?             $1                                        0.683




               Year START                    INTEREST               END
                      1     $0.683              $0.068              $0.751
                      2     $0.751              $0.075              $0.826
                      3     $0.826              $0.083              $0.909
                      4     $0.909              $0.091              $1.000
The Present Value of $1

  10% Semi-annual Compounding                      4 years
Present     Future Single            times             Factor
Value =       Amount                               I = 5%, n = 8

   ?             $1                                     0.677




              Period START                   INTEREST              END
                      1     $0.677             $0.034              $0.711
                      2     $0.711             $0.036              $0.746
                      3     $0.746             $0.037              $0.784
                      4     $0.784             $0.039              $0.823
                      5     $0.823             $0.041              $0.864
                      6     $0.864             $0.043              $0.907
                      7     $0.907             $0.045              $0.953
                      8     $0.953             $0.048              $1.000
Compounding Matters

The More Compounding Periods Per Year, The Higher the Effective
or Equivalent Interest Per Year
What will a $1 deposit at the start of the year grow to at 10% annual interest
with different compounding periods?

                                                     Effective
                                                   Annual Interest
          Compounding Periods         Start            Rate                 End

                  Annual                $1.00           10.0000%          $1.100000
                  Semi-Annual           $1.00           10.2500%          $1.102500
                  Quarterly             $1.00           10.3813%          $1.103813
                  Daily                 $1.00           10.5156%          $1.105156
                  Continuous            $1.00           10.5171%          $1.105171
The Future Value Annuity of $1

10.00% Semi-annual compounding                  4 years    is equivalent to
10.25% annual compounding                       4 years

Future          Future Periodic         times               Factor      `
Value =            Amount                             I = 10.25%, n = 4

   ?                  $1                                    4.658




 Year       START           INTEREST             Balance             Deposit   END
        1    $0.000            $0.000             $0.000              $1.000   $1.000
        2    $1.000            $0.103             $1.103              $1.000   $2.103
        3    $2.103            $0.216             $2.318              $1.000   $3.318
        4    $3.318            $0.340             $3.658              $1.000   $4.658


10% annual interest compounded semi-annual is equivalent to 10.25% per annual compounding
The Future Value Annuity of $1

  10% Annual Compounding                     4 years
Future        Future Periodic        times                  Factor       `
Value =          Amount                                I = 10%, n = 4

   ?                $1                                     4.641




 Year START              INTEREST             Balance              Deposit       END
       1   $0.000           $0.000              $0.000                  $1.000   $1.000
       2   $1.000           $0.100              $1.100                  $1.000   $2.100
       3   $2.100           $0.210              $2.310                  $1.000   $3.310
       4   $3.310           $0.331              $3.641                  $1.000   $4.641
The Present Value Annuity of $1

  10% Annual Compounding                     4 years
Present       Future Periodic        times                  Factor       `
Value =          Amount                                I = 10%, n = 4

   ?                $1                                      3.17




 Year START              INTEREST             Balance              Withdraw      END
       1   $3.170           $0.317              $3.487                  $1.000   $2.487
       2   $2.487           $0.249              $2.736                  $1.000   $1.736
       3   $1.736           $0.174              $1.909                  $1.000   $0.909
       4   $0.909           $0.091              $1.000                  $1.000   $0.000
The Future Value of $1
    10% Semi-annual Compounding             4 years

Future       Present Single         times                 Factor
Value =         Amount                                I = 5%, n = 8

   ?              $1                                      1.477




                Period START                INTEREST                  END
                       1   $1.000              $0.050                 $1.050
                       2   $1.050              $0.053                 $1.103
                       3   $1.103              $0.055                 $1.158
                       4   $1.158              $0.058                 $1.216
                       5   $1.216              $0.061                 $1.276
                       6   $1.276              $0.064                 $1.340
                       7   $1.340              $0.067                 $1.407
                       8   $1.407              $0.070                 $1.477
The Future Value of $1

   10% annual compounding,                 4 years


Future      Present Single         times                  Factor
Value =        Amount                                I = 10%, n = 4

   ?             $1                                      1.464




              Year        START            INTEREST               END
                      1   $1.000              $0.100              $1.100
                      2   $1.100              $0.110              $1.210
                      3   $1.210              $0.121              $1.331
                      4   $1.331              $0.133              $1.464
The Present Value Annuity of $1

 10.00% Semi-annual compounding                 4 years    is equivalent to
 10.25% Annual compounding                      4 years

Present        Future Periodic          times               Factor      `
Value =           Amount                              I = 10.25%, n = 4

   ?                 $1                                     3.153



                             10.25%
Year       START           INTEREST              Balance            Withdraw   END
       1    $3.153             $0.323             $3.476              $1.000   $2.476
       2    $2.476             $0.254             $2.730              $1.000   $1.730
       3    $1.730             $0.177             $1.907              $1.000   $0.907
       4    $0.907             $0.093             $1.000              $1.000   $0.000


10% annual interest compounded semi-annual is equivalent to 10.25% per annual compounding

				
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