Mrs$.$ Williams finds that she has two options for investing $$32,000\mathrm{.}02$ for fif$-$

teen years. The first option is to deposit the $$32,000\mathrm{.}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 $d(4).$