Future Value of an Annuity - Download as DOC by tfl17769

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									                Future Value of an Annuity
Definitions

An annuity is a series of equal money payments for a specified number
of periods (weeks, months, years).

An ordinary annuity has the payments made at the end of the periods.
An annuity due has the payments made at the beginning of the periods.

Ordinary annuities are much more common than annuities due. If only
“annuity” is used, it is assumed to mean ordinary annuity.


Calculating Future Values of Annuities

Decomposing the annuity. Each cash flow can be treated separately
using the formulas for compounding single amounts. Then each of the
individual future values would be added together to get the total future
value of the entire annuity.




                                Table 5.5
                                    -2-




Using tables.

                    FVAn      =    PMT(FVIFAi,n)

    Example: What is the future value of a 5-year $500.00 ordinary
             annuity compounded at 6% annually?

                    FVAn      = PMT(FVIFAi,n)
                    FVAn      = 500.00(FVIFA6%,5 yr)
                    FVAn      = 500.00(5.6371)              [alternate table]

                    FVAn      = $ 2,818.55


                What is the future value of a 5-year $500.00 annuity due
                compounded at 6.00% annually?

                    FVA(due)n      =   PMT(FVIFAi,n)(1 + i)
                    FVA(due)n      =   2,818.55(1+ .06)
                    FVA(due)n      =   2,818.55(1.06)
                    FVA(due)n      = $ 2,987.66
                                   -3-



Using cash flow analysis tables.


Ordinary Annuity

     Time Cash Flow            Interest Factor       Future Value
       0         0            1.065 = 1.3382256          0
       1    500.00            1.064 = 1.262477          631.24
       2    500.00            1.063 = 1.191016          595.51
       3    500.00            1.062 = 1.1236            561.80
       4    500.00            1.061 = 1.06              530.00
       5    500.00            1.060 = 1                 500.00
                                                       ----------
                                                    $ 2,818.55

Annuity Due

     Time   Cash Flow          Interest Factor   Future Value
                                   5
       0      500.00          1.06 = 1.3382256 669.11
       1      500.00          1.064 = 1.262477      631.24
       2      500.00          1.063 = 1.191016      595.51
                                   2
       3      500.00          1.06 = 1.1236         561.80
                                   1
       4      500.00          1.06 = 1.06           530.00
                                   0
       5           0          1.06 = 1                     0
                                                   ----------
                                                $ 2,987.66


Note that the annuity due produces the larger future value. The earlier
the cash flow is received, the more time it has to accumulate interest.

								
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