Question

An arithmetic cash flow gradient series equals $600 in year 1, $700 in year 2, and amounts increasing by $100 per year through year 9. At i = 9% per year, determine the present worth of the cash flow series in year 0.
The present worth of the cash flow series in year 0 is $
The question is properly stated and nothing is wrong with it!

Answer 1

Answer:

Present value ofthe annuity 6,163.14

Explanation:

We build the schedule of the annuity:

#  Beginning / Installment / Total / Interst / Ending

1                       600 600 1.09      654

2    654         700         1354 1.09     1,475.86

3   1475.86 800 2275.86 1.09    2,480.69

4  2480.69 900 3380.69 1.09    3,684.95

5  3684.95 1000 4684.95 1.09    5,106.6

6  5106.6 1100 6206.6 1.09    6,765.19

7  6765.19 1200 7965.19 1.09    8,682.06

8 8682.06 1300 9982.06 1.09   10,880.45

9 10880.45 1400 12280.45 1.09   13,385.69

Then we discount the future value at 9% to get the present value:

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  $13,385.6900

time  9.00

rate  0.09000

$\frac{13385.69}{(1 + 0.09)^{9} } = PV$  

PV   6,163.1435