The present worth of an increasing geometric gra­dient is $23,632. The interest rate is 6% per year and the rate of change series is 4% per year. If the cash flow in year 1 is $3,000, the year in which the gradient ends is:

(a) 7
(b) 9
(c) 11
(d) 12


23,632 = 3000{1- [(1+0.04)n/(1+0.06)n]}/(0.06-0.04)
[(23,632*0.02)/3000]-1 = (0.98113)n
log 0.84245 = nlog 0.98113
n = 9
Answer is (b)

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