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Math Help - compound interest

  1. #1
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    compound interest

    if $500 was invested at 8%/a, compounded annually, in one account, and $600 was invested at 6%/a, compounded annually, in another account, then when would the amounts in both accounts be equal?
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  2. #2
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    Quote Originally Posted by imthatgirl View Post
    if $500 was invested at 8%/a, compounded annually, in one account, and $600 was invested at 6%/a, compounded annually, in another account, then when would the amounts in both accounts be equal?
    The amount in the first account after n years is:

    B1=500*(1.08)^n,

    and in the second account:

    B2=600*(1.06)^n.

    These are equal when:

    B1=B2,

    or:

    500*(1.08)^n=600*(1.06)^n

    Rearranging:

    (1.08/1.06)^n=600/500,

    taking logs:

    n log(1.08/1.06)=log(600/500),

    or:

    n=log(600/500)/log(1.08/1.06)=9.75 years,

    But as the interest is paid yearly they will in fact never be equal, but
    are most nearly equal after 10 years, when the accounts contain
    $1079.46 and $1074.50 respectively.

    RonL
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