Calculate the present worth of a geometric gradient series with a cash flow of $35,000 in year 1 and increases of 5% each year through year 6. The interest rate is 10% per year.

$145,038.567

Explanation:

Solution

Let

g = gradient percent (as a decimal in calculations)

i = interest percent (as a decimal in calculations)

n = number of periods

A1 = payment at EOY 1

A1 = $35,000; g = 5%; i = 10%; n = 6

Hence:

P = A1 ( P/ A1, g, i, n ) = 100 [ 1 – ( 1 + 0.05 )^5( 1 + 0.1 )^ –5 ] / ( 0.1 – 0.05 )

= $35000 [ 1 – 1.276815625 * 0.6209213230] / (0.05)

= $35000 [ 0.2071979529] / (0.05)

Therefore the present value  or worth of the geometric gradient series is

= $145,038.567

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