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Math Help - Interest, compounded quarterly..

  1. #1
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    Interest, compounded quarterly..

    I am unsure/unaware of the formula and how to use it to complete this problem. Any help is greatly appreciated.

    Art invests $2700 in a savings account that pays 9% interest, compounded quarterly. if there are no other transactions, when will his balance reach $4550?
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  2. #2
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    Quote Originally Posted by Wesker View Post
    I am unsure/unaware of the formula and how to use it to complete this problem. Any help is greatly appreciated.

    Art invests $2700 in a savings account that pays 9% interest, compounded quarterly. if there are no other transactions, when will his balance reach $4550?
    Use this formula:
    P(t) = P_0\left(1 + \frac{r}{k}\right)^{kt}, where

    P_0 is the initial amount,
    r is the interest in decimal,
    k is the number of times per year the interest is compounded, and
    t is the time in years.

    The equation for the above problem would then be
    4550 = 2700\left(1 + \frac{0.09}{4}\right)^{4t},
    then solve for t.


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  3. #3
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    A little bit of an explanation of the formula yeongil gave: If the interest rate is r per year, then it is r/k every "kth" of a year. That is, each "kth" of a year, for principal P, we calculate (r/k)P and add it to P: P+ (r/k)P= P(1+ r/k). Every "kth of a year" we multiply by that (1+ r/k). Since there are k "kths" in a year, in t years, we will have multiplied kt times. Multiplying by the same thing kt times is the same as multiplying by (1+ r/k)^{kt}, thus yeongil's formula: P(1+ r/k)^{kt}.
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