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A cash flow at time zero​ (now) of ​$ is equivalent to another cash flow that is an EOY annuity of ​$ over years​ (starting at year​ 1). Each of these two​ cash-flow series is equivalent to a third​ series, which is a uniform gradient series. What is the value of G for this third series over the same ​-year time​ interval? Assume that the cash flow at the end of year one is zero.

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Answer:

$1,354

Explanation:

The computation of the value of G for the third series over the same year interval is shown below:

Zero time cash flow = End of the year annuity amount × ((P/A, i, 5)

$9,982 = $2,500 × (P/A, i, 5)

where,

i = 8 per year

$9,982 = G × (P/G, 8%, 5) = 7.372

G = $9,982 ÷ 7.372

= $1,354

Hence, the value of G for this third series over the same year time interval is $1,354

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