Becky Hilton has a choice for her investment of $$$$7,500.$ She can invest it in funds she believes will earn either $($a$)6\%$ compounded quarterly for $3$ years or $($b$)12\%$ compounded semiannually for $7$ years. Find the future value of both. $($c$)$ Which is$$ larger?

Part $1$

$($a$)$ The future value of her investment is $$$

enter your response here.

$($Round to the nearest cent as$$ needed.$)$