Gavin deposited money into his savings account that is compounded annually at an interest rate of 9%. Gavin thought the equivalent quarterly interest rate would be 2.25%. Is Gavin correct? If he is, explain why. If he is not correct, state what the equivalent quarterly interest rate is and show how you got your answer

Gavin is correct. This problem is about converting 9% per year to how many percent per quarter. The rate is still the same. It only differed in the time period. So, through dimensional analysis,

9% per year * (1 year / 4 quarters) = 2.25% per quarter

If he was asked to convert 9% per year to how many percent per quarter compounded quarterly, then you will not simply divide by four. This is because compounding is not linear.