Lloyd is a divorce attorney who practices law in Florida. He wants to join the American Divorce Lawyers Association (ADLA), a professional organization for divorce attorneys. The membership dues for the ADLA are $800 per year and must be paid at the beginning of each year. For instance, membership dues for the first year are paid today, and dues for the second year are payable one year from today. However, the ADLA also has an option for members to buy a lifetime membership today for $8,500 and never have to pay annual membership dues. Obviously, the lifetime membership isn't a good deal if you only remain a member for a couple of years, but if you remain a member for 40 years, it's a great deal. Suppose that the appropriate annual interest rate is 7.6%. What is the minimum number of years that Lloyd must remain a member of the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $800 in annual membership dues? a. 14 years b. 13 years c. 19 years d. 23 years

The Question has been offered as to pick the least of the terms less expensive than lifetime alternative, so it is smarter to continue with the choices given in the Question.

For 14 years:

Year                Cash Flow                  PVF = 7.6%            Cash Flow

0                      $800                                 1                            $800

1 - 13                $800                             8.0807                   $6464.56

                                                                 Total                    $7264.56

For 13 years :

Year                Cash Flow                  PVF = 7.6%            Cash Flow

0                       $800                                1                            $800

1 - 12                 $800                            7.6948                   $6155.83

                                                              Total                    $6955.835

For 19 years

Year                Cash Flow                  PVF = 7.6%            Cash Flow

0                        $800                               1                            $800

1 - 18                  $800                            9.6377                   $7710.16

                                                              Total                      $8510.16

For the long time alternative it is realize that not doable choice to go with 19 years so obviously past 19 years likewise not possible so for a long time not comprehended.  

from the over the least is accessible in 13 years so lloyd needs to go for a long time.