Today, Barry reached his $50$th birthday and he has $$70,000$ in his retirement fund. His goal is to have $$500,000$ on his $65$th birthday. He can expect his investments to earn $13\%$ compounded semiannually. How much will he have to invest at the end of every six months for the next $15$ years in order to reach his goal?

Group of answer choices

$$1,722\mathrm{.}84$

$$4,978\mathrm{.}30$

$$428\mathrm{.}30$

$$926\mathrm{.}14$

$$2,388\mathrm{.}89$