Foundations of Financial Management: An Analysis (part 27)

“Money never made a man happy yet, nor will it. The more a man has, the more he wants. Instead of filling a vacuum, it makes one.”

- Benjamin Franklin

The Time Value of Money (Part B)

by

Charles Lamson

Future Value---Annuity

Our calculations up to now have dealt with single amounts rather than an annuity, which may be defined as a series of consecutive payments or receipts of equal amount. The annuity values are generally assumed to occur at the end of each period. If we invest $1,000 at the end of each year for four years and our funds grow at 10%, what is the future value of this annuity? We may find the future value for each payment and then total them to find the future value of an annuity (Figure 2).

Figure 2 (Assumption for annuity is that 1st payment doesn't come till end of first year.)

The future value for the annuity in Figure 2 is $4,641. Although this is a four period annuity, the first $1,000 comes at the end of the first period and has but three periods to run, the second $1,000 at the end of the second period, with two periods remaining---and so on down to the last $1,000 at the end of the fourth period. The final payment (period 4) is not compounded at all.

Because the process of compounding the individual values is tedious, special tables are also available for annuity computations. We shall refer to Table 3 above, the future value of an annuity of $1. Let us define A as the annuity value and use Formula 3 for the future value of an annuity. Note that the A part of the subscript on both the left- and right-hand side of the formula below indicates we are dealing with tables for an annuity rather than a single amount. Lamont. Using Table 3 for A = $1,000, and n = 4, and i = 10%:

If a wealthy relative offered to set aside $2,500 a year for you for the next 20 years, how much would you have in your account after 20 years if the funds grew at 8 percent? The answer is as follows:

A rather tidy sum considering that only a total of $50,000 has been invested over the 20 years.

Present Value---Annuity

To find the present value of an annuity, the process is reversed. In theory each individual payment is discounted back to the present and then all of the discounted payments are added up, yielding the present value of the annuity.

Table Four allows us to eliminate extensive calculations and to find our answer directly.

*MAIN SOURCE: BLOCK & HIRT, 2005, FOUNDATIONS OF FINANCIAL MANAGEMENT, 11TH ED., PP. 242-245*

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