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23 August, 06:13

Rebecca deposited money into his retirement account that is compounded annually at an interest rate of 7%. Rebecca thought the equivalent quarterly interest rate would be 2%. Is Rebecca correct? If she is, explain why. If she is not correct state what the equivalent quarterly interest rate is and show how you got your answer.

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  1. 23 August, 07:39
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    Rebecca is incorrect. The equivalent quarterly interest rate is 1.75%.

    Explanation:

    The formula for compound interest is i = r/n.

    r represents the interest rate in decimal form.

    n represents the compounding periods in a year.

    Calculate the interest rate for 7% compounded quarterly:

    Since interest compounded quarterly is four times a year, n = 4.

    7% is converted to decimal form by dividing by 100.

    7 / 100 = 0.07

    r = 0.07

    Substitute these into the formula:

    i = r/n

    = 0.07/4

    = 0.0175

    0.0175 is in decimal form. To convert it to a percentage, multiply it by 100.

    0.0175 X 100 = 1.75%

    1.75% ≠ 2%

    Therefore, Rebecca is incorrect. The equivalent quarterly interest rate is 1.75%.
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