Appendix A 217A = $1811.70
Factors are also available for the relationships between a future
worth (accumulated amount) and a uniform series. The factor (F|A,i,n)
is known as the uniform series future worth factor and is read “to find F
given A at i% for n years.” The reciprocal factor, (A|F,i,n), is known as
the uniform series sinking fund factor and is read “to find A given F at i%
for n years.” An important observation when using an (F|A,i,n) factor
or an (A|F,i,n) factor is that the “F” resulting from the calculation oc-
curs at the same point in time as to the last “A” cash flow. The algebraic
expressions for (A|F,i,n) and (F|A,i,n) are shown in Table 6 at the end
of this section.
Example 10
If you deposit $2000 per year into an individual retirement account
starting on your 24th birthday, how much will have accumulated in the
account at the time of your deposit on your 65th birthday? The account
pays 6%/yr.
n = 42 (birthdays between 24th and 65th, inclusive)
F = A * (F|A,6%,42)
F = 2000 * (175.9505) = $351,901
Example 1 1
If you want to be a millionaire on your 65th birthday, what equal an-
nual deposits must be made in an account starting on your 24th birthday?
The account pays 10%/yr.
n = 42 (birthdays between 24th and 65th, inclusive)
A = F * (A|F,10%,42)
A = 1000000 * (0.001860) = $1860
A.6.8 Gradient Series
A gradient series of cash flows occurs when the value of a given cash
flow is greater than the value of the previous period’s cash flow by a con-
stant amount. The symbol used to represent the constant increment is G.
The factor (P|G,i,n) is known as the gradient series, present worth factor.