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28 September, 09:16

ou make $9,300 annual deposits into a retirement account that pays an APR of 9.9 percent compounded monthly. How large will your account balance be in 30 years

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  1. 28 September, 09:56
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    Acct. Balance in 30 years.

    F = $1637953.99

    Explanation:

    EAR = [ (1 + (r/n)) ^n] - 1

    Where EAR = effective annual rate

    r = rate = 9.9% = 0.099

    n = 12 monthly compounding interest

    So therefore:

    EAR = (1 + (.099/12)) ¹² - 1 = 0.1036 = 10.36%

    To calculate how large the acct. Balance will be, we have

    F = A*[ ((1 + i) ^n) - 1) / i]

    Where f = future value of investment.

    A = annual investment value = 9300

    i = EAR =.1036

    n = 30

    F = 9300 * [ ((1 + 0.1036) ^30 - 1) / 0.1036]

    F = $1637953.99
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