$765.13 is deposited at the end of each month for 3 years in an account paying 2% Interest compounded monthly. Find the final amount of the

Question

$765.13 is deposited at the end of each month for 3 years in an account paying 2% Interest compounded monthly. Find the final amount of the account. Round to the nearest
cent
O A. $27,598.32
OB. $28,363,45
OC. $29,128.58
OD. $26,787.27

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Brielle 1 week 2021-09-14T05:56:46+00:00 1 Answer 0

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    2021-09-14T05:58:19+00:00

    Answer:

    Option B.

    Step-by-step explanation:

    The future value formula, for an annuity, is:

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

    An annuity means that a number of payments happen during the period(an year, for example).

    P is the value of the deposit, r is the interest rate, as a decimal, and n is the number of deposits.

    In this question:

    Deposits of $765.13, so P = 765.13

    Each month, for 3 years. An year has twelve months, so n = 3*12 = 36

    2% Interest a year. An year has 12 months, so r = \frac{0.02}{12} = 0.00167

    Find the final amount of the account.

    FV = \frac{765.13*((1 + 0.00167)^{36} - 1)}{0.00167} = 28,363.46

    The final amount of the account will be $28,363.46, which is option B.

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