Question

Gavin deposited money into his savings account that is compounded annually at an interest rate of 9%. He 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.

Answer 1

Gavin confused the simple division of the annual rate by the number of quarters with the correct method of determining the equivalent quarterly rate. The correct quarterly interest rate equivalent to an annual rate of 9% compounded annually is approximately 2.206%, determined by the formula (1 + 0.09)^(1/4) - 1.

Step-by-step explanation:

Gavin is not correct about the equivalent quarterly interest rate. If an account is compounded annually at a 9% rate, the equivalent quarterly interest rate is found using the formula for converting annual interest rates to other compounding periods:

(1 + annual rate)^1/n - 1, where n is the number of compounding periods per year.

For quarterly compounding, n = 4. So the calculation is (1 + 0.09)^(1/4) - 1, which is approximately 2.206% per quarter, not 2.25%.

Here is the detailed calculation:

(1 + 0.09)^(1/4) = (1.09)^(0.25)

(1.09)^(0.25) ≈ 1.02206

1.02206 - 1 = 0.02206

0.02206 × 100 = 2.206%

Answer 2

Answer:4%

Step-by-step explanation: i dont have enough time to write paragraph sorry, gotta leave in 5 min.