Jared Goff just received an inheritance of $$35,775$ from his great aunt. He plans to invest the funds for retirement. If Mr$.$ Goff can earn $4\mathrm{.}75\%$ per year with quarterly compounding for $32$ years, how much will he have accumulated?

Group of answer choices

$$90,153\mathrm{.}00$

$$157,946\mathrm{.}01$

$$160,690\mathrm{.}49$

$$162,113\mathrm{.}25$

$$163,555\mathrm{.}18$