The present worth "P" calculated for the arithmetic gradient series below, using equation: PG = -100(P/G,i%,4) should be in year
An arithmetic gradient cash flow is when the cash flow changes by the same amount (increases or decreases) in each cash flow period. For example, if the cash flow in period 1 is $800 and the cash flow in period 2 is $900, with amounts increasing by $100 in each subsequent period, this is an arithmetic gradient cash flow series with a gradient, G, of $100. P = G (P/G, i,n) is the standard factor notation equation for the present value of an arithmetic gradient cash flow. This equation calculates the current value of only the gradient (the $100 increases in the preceding example), not the base amount of money on which the gradient was built (the $800 in the previous example). As a uniform cash flow series, the base amount in period one must be handled separately. The general equation for calculating the present value of an arithmetic gradient cash flow series is as follows:
P = present value of the base amount + current value of the gradient amount
A (P/A,i,n) + G (P/G, i,n) = A (P/A,i,n) + G (P/G, i,n)
where:
A = the total amount of money in period 1.
G = the difference in amount between periods 1 and 2.
n = the number of periods from 1 to the end of the gradient
I = period interest rate
If the gradient cash flow decreases rather than increases from one period to the next, the only change in the general equation is that the plus sign becomes a minus sign.
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