Appendix A 213amount, i is an interest rate (expressed as a percentage amount), and n de-
notes a number of years. The factor (F|P,i,n) is read “to find F given P at i%
for n years.” Tables of values of (F|P,i,n) for selected values of i and n are
provided in Appendix 4A. The tables of values in Appendix 4A are orga-
nized such that the annual interest rate (i) determines the appropriate page,
the time value of money factor (F|P) determines the appropriate column,
and the number of years (n) determines the appropriate row.
Example 5
Repeat Example 4 using the single sum, future worth factor.
Fn = P * (1 + i)n
Fn = P * (F|P,i,n)
F 4 = 500 * (F|P,10%,4)
F 4 = 500 * (1.4641)
F 4 = 732.05
The above formulas for compound interest allow us to solve for an
unknown F, given P, i, and n. What if we want to determine P with known
values of F, i, and n? We can derive this relationship from the compound
interest formula above:
Fn = P (1+i)n
Dividing both sides by (1+i)n yieldsFn
P = ————
(1 + i)n
which can be rewritten as
P = Fn (1+i)–nThe factor (1+i)–n is known as the single sum; present worth factor; or
the single payment, present worth factor. This factor is denoted (P|F,i,n)
and is read “to find P given F at i% for n years.” Tables of (P|F,i,n) are
provided in Appendix 4A.
Example 6
To accumulate $1000 five years from today in an account earning
8%/yr compound interest, how much must be deposited today?