A friend wants to borrow money from you. He states that he will pay you $$4,000$ every $6$ months for $8$ years with the first payment exactly $3$ years and six months from today. The interest rate is an APR of $6\mathrm{.}3$ percent with semiannual compounding. What is the value of the payments today?

Multiple Choice

$$41,238\mathrm{.}74$

$$41,354\mathrm{.}33$

$$42,613\mathrm{.}37$

$$31,069\mathrm{.}04$