Appendix A 215For the $500 deposit n = 4, for the $600 deposit n = 8
P = 500 (P|F,6%,4) + 600 (P|F,6%,8)
P = 500 (0.7921) + 600 (0.6274)
P = 396.05 + 376.44 = $772.49
A.6.7 Uniform Series Cash Flows
A uniform series of cash flows exists when the cash flows are in a
series, occur every year, and are all equal in value. Figure A-3 shows the
cash flow diagram of a uniform series of withdrawals. The uniform series
has length 4 and amount 2000. If we want to determine the amount of
money that would have to be deposited today to support this series of
withdrawals, starting one year from today, we could use the approach
illustrated in Example 8 above to determine a present worth component
for each individual cash flow. This approach would require us to sum the
following series of factors (assuming the interest rate is 9%/yr):
P = 2000(P|F,9%,1) + 2000(P|F,9%,2) +
2000(P|F,9%,3) + 2000(P|F,9%,4)
After some algebraic manipulation, this expression can be restated as:
P = 2000[(P|F,9%,1) + (P|F,9%,2) +
(P|F,9%,3) + (P|F,9%,4)]
P = 2000[(0.9174) + (0.8417) + (0.7722) + (0.7084)]
P = 2000*[3.2397] = $6479.40
Figure A-3. Uniform series cash flowFortunately, uniform series occur frequently enough in practice to
justify tabulating values to eliminate the need to repeatedly sum a series
of (P|F,i,n) factors. To accommodate uniform series factors, we need to
add a new symbol to our time value of money terminology in addition
to the single sum symbols P and F. The symbol “A” is used to designate