The future worth in year 8 for the cash flows shown is $20,000. At an interest rate of 10% per year, what is the value, x, of the cash flow in year 4?
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Move $20,000 to year 0, add and subtract $1600 in year 4 to use gradient, and solve for x. Use + signs for cash flows for convenience.
20,000(P/F,10%,8) = 1000(P/A,10%,8) + 200(P/G,10%,8) – 1600(P/F,10%,4)
+ x(P/F,10%,4)
20,000(0.4665) = 1000(5.3349) + 200(16.0287) – 1600(0.6830) + x(0.6830)
9330 = 5334.90 + 3205.74 – 1092.80 + 0.683x
x = $2755.72
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