Gavin deposited money into his savings account that is compounded annually at an interest rate of 9%. Gavin thought the equivalent quarterly

Question

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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Helga 3 years 2021-08-22T17:00:04+00:00 1 Answers 26 views 0

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  1. Edana
    0
    2021-08-22T17:01:09+00:00
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    Answer:

    The equivalent rate is of 0.093 = 9.3% a year. Gavin is wrong, because he applied the wrong formula, its not just dividing the interest rate r by the number of compoundings n, it is E = (1 + \frac{r}{n})^{n} - 1

    Step-by-step explanation:

    Equivalent interest rate:

    The equivalent interest rate for an amount compounded n times during a year is given by:

    E = (1 + \frac{r}{n})^{n} - 1

    In which r is the interest rate and n is the number of compoundings during an year.

    Compounded annually at an interest rate of 9%

    This means that r = 0.09

    Compounded quarterly:

    This means that n = 4

    Equivalent rate:

    E = (1 + \frac{0.09}{4})^{4} - 1 = 0.093

    The equivalent rate is of 0.093 = 9.3% a year. Gavin is wrong, because he applied the wrong formula, its not just dividing the interest rate r by the number of compoundings n, it is E = (1 + \frac{r}{n})^{n} - 1

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