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Unit 2: Time Value of Money



              Interest for second quarter (  1015 × 0.06 × 1 × 1/4)  15.23                        Notes

              Amount available at end of second quarter         1030.23
              Interest for third quarter (  1030.23 × 0.06 × 1 × 1/4)  15.45
              Amount available at end of third quarter          1045.68

              Interest for fourth quarter (  1045.68 × 0.06 × 1 × 1/4)  15.69
              Amount available at end of first year             1061.37
            With quarterly compounding, the initial investment of   1000 earned   1.37 more interest in the
            first year than with annual compounding. Compound interest is defined with the following
            terms:
                      P = principal sum earns

                      i = interest rate per period
                      n = number of period during which compounding takes place – a period can be
                          any length in time

            Future Value of   1
            A sum of money invested today at compound interest accumulates to a larger sum called the
            amount or future value. The future value of   1000 invested at 6% compounded annually for
            2 years is   1123.60. The future value includes the original principal and the accumulated interest.




               Notes  The future value varies with the interest rate, the compounding frequency and the
              number of periods.
            If the future value of   1 principal investment is known, we can use it to calculate the future value
            of any amount invested. For example, at 8% interest per period,   1 accumulates as follows:
                     Future value of   1 at 8% for 1 period =   1.00000 × 1.08 =   1.08000
                     Future value of   1 at 8% for 2 periods =   1.08000 × 1.08 =   1.16640
                     Future value of   1 at 8% for 3 periods =   1.16640 × 1.08 =   1.25971
            The above can be diagrammed as follows:
            Interest is added to principal at the end of each period
                                              Figure  2.1













            The end of each period is designated by a grey cylinder like figure. The arrows pointing to the
            end of each period indicate that payments are made into the investment. The general formula
            for the future value of   1, with n representing the number of compounding period is
                     fv = (1 + i)n




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