3. 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.

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Step-by-step explanation:

If the money Gavin deposited were subject to 9% interest compounded quarterly, then the equivalent quarterly rate would be 9%/4 = 2.25%.

However, that is not the case.

Rather, the quarterly rate (r) will have an effective annual rate of (1+r)^4 -1. If we want that effective annual rate to be 9%, then we can find the quarterly rate from ...

  (1 +r)^4 -1 = 0.09

  (1 +r)^4 = 1.09 . . . . . add 1

  1 +r = 1.09^(1/4) . . . . . take the 4th root

  r = 1.09^(1/4) -1 ≈ 0.0217782

The equivalent quarterly rate is about 2.178%.

The equivalent quarterly rate is about 2.178%.

 (1 +r)^4 -1 = 0.09

  (1 +r)^4 = 1.09 . . . . . add 1

 1 +r = 1.09^(1/4) . . . . . take the 4th root

 r = 1.09^(1/4) -1 ≈ 0.0217782.

Step-by-step explanation:

the correct answer is c

good luck love

i think its a.

hope this