Ian wanted to ensure that she had $$65,000$ for her child's university education. As soon as her child was born, she started saving $$1,175$ every $6$ months in an investment fund. If she achieved her investment target on her child's $18$th birthday, and she made no deposit on the child's $18$th birthday, calculate the following:

a$.$ The nominal interest rate for the investment, compounded quarterly.

$\%$

Round to two decimal places.

b$.$ Calculate the effective interest rate for this investment.

$\%$

Round to two decimal places.