Question

The future worth in year 10 of an arithmetic gradient cash flow series for years 1...

The future worth in year 10 of an arithmetic gradient cash flow series for years 1 through 10 is $675,000. If the gradient increase each year, G, is $1500, determine the cash flow in year 1 at an interest rate of 10% per year.

The cash flow in year 1 is $

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Answer #1

The present value of future worth.

The present value of the future worth of the arithmetic gradient cash flow is calculated below:

P = F( P / F,i,n)

675000 (P / F ,0.1,10)

=675000 / (1 + 0.1)10

= 260,241.72.

The present value equates the sum of cash flow per year and the gradient:

P = A(P / A,i,n) + G (P / G,i,n)

260,241.72 = A (P / A,i,n) + 1500 (P / G 0.1,10)

260,241.72 = (A * 6.14456) + (1500 * 22.8913)

260241.72 = (A * 6.14456) + 34336.95

260241.72 - 34336.95 = (A * 6.14456)

A = (225904.77 / 6.14456)

A = 36,765

Therefore, the cash flow in the year 1 is 36,765

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