Mrs. Williams finds that she has two options for investing $32,000.02 for fifteen years. The first option is to deposit the $32,000.02 into a fund earning a nominal rate of discount d(4) payable quarterly. The second option is to purchase an annuity-immediate with 15 level annual payments, the annuity payments computed using an annual effective rate of 7%, and then when she gets an annuity payment, to immediately invest it into a fund earning an annual effective rate of 5%. Mrs. Williams calculates that the second option produces an accumulated value that is $1,500 more than the accumulated value yielded by the first option. Calculate d(4).