Compounding Interest by gza74461

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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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