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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 $750,000. If the gradient increase each year, G, is $2250, determine the cash flow in year 1 at an interest rate of 6% per year.

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Expert Solution

Cash Flow in Year 1= 47,851

PV of incremental Cash Flow + PV of Cash Flows = Present Value of Future Worth
                                                  66,605 + Cashflow*7.3600871 = 750000*0.5583948
                                                  66,605 + Cashflow*7.3600871 =                                                 418,796
Cashflow = (418796-66605)/7.3600871
Cashflow =                                             47,851
Year Incremental Cash Flow Present Value Factor Present Value
1                       -   0.9433962                   -  
2          2,250.00 0.8899964            2,002
3          4,500.00 0.8396193            3,778
4          6,750.00 0.7920937            5,347
5          9,000.00 0.7472582            6,725
6        11,250.00 0.7049605            7,931
7        13,500.00 0.6650571            8,978
8        15,750.00 0.6274124            9,882
9        18,000.00 0.5918985          10,654
10        20,250.00 0.5583948          11,307
7.3600871          66,605


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