The annual worth for years 1 through 8 of the cash flows shown is $30,000. What is the amount of x, the cash flow in year 3, at i = 10% per year? Solve using (a) tabulated factors, and (b) a spreadsheet.
(a) Add and subtract $2400 and $2600 in periods 3 and 4, respectively, to use gradient
factors. Use + signs for cash flows for convenience.
30,000 = 2000 + 200(A/G,10%,8) – 2400(P/F,10%,3)(A/P,10%,8)
-2600(P/F,10%,4)(A/P,10%,8) + x(P/F,10%,3)(A/P,10%,8)
+ 2x(P/F,10%,4)(A/P,10%,8)
30,000 = 2000 + 200(3.0045) – 2400(0.7513)( 0.18744)
-2600(0.6830)( 0.18744) + x(0.7513)(0.18744)
+ 2x(0.6830)( 0.18744)
Solution continued on the next page...
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30,000 = 2000 + 600.90 – 337.98 – 332.86 + 0.14082x + 0.25604x
0.39686x = 28,069.94
x = $70,730
(b) Spreadsheet uses Goal Seek to find x = $70,726
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