P ¼ F n
1
1 þ r
ð
Þ
n
(10)
The reciprocal factor is also called the (P/F) factor or the “present worth factor for a
single sum” (PWFS). Thus,
P ¼ F P=F
ð
Þ
r
n
(11)
Or
P ¼ F PWFS
ð
Þ
r
n
(12)
In all these formulas, the compounding becomes effective at the end of the period.
This is true in all the expressions used in economic calculations; modified formulas are
needed if the compounding becomes effective at the beginning of the period, but this is
seldom, if ever, the case. The formula modification, if needed, involves a (1 + r) factor.
Future Value of a Uniform Series of Payments (Made at the End
of Each Period)
See Appendices 9 and 10 for justification.
If the amount paid at the end of each period is A, the future value, F n , of the sum
is given by
F n ¼ A
1 þ r
ð
Þ
n À 1
r
(13)
The multiplier is also known as the (F/A) factor or the “compound amount factor for
a uniform series” (CAFUS).
F ¼ A F=A
ð
Þ
r
n
(14)
Or
F ¼ A CAFUS
ð
Þ
r
n
(15)
Sinking Funds
A sinking fund consists of a series of payments made for the purpose of accumulating a given amount of money, F, at some future time. As usual, we assume a
uniform series of payments, A being the amount paid at the end of each period. The
calculation assumes that the rate of interest does not change over time; trial and
error would be required otherwise.
768
D.S.J. Jones and P.R. Pujado ´