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Math Help - Number problem

  1. #1
    Junior Member
    Joined
    Oct 2007
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    Number problem

    PLease help me with this problem as I am stuck...


    Jemima has $5000 to invest for two and a half years.
    Her bank offers two different investment schemes:

    Scheme 1
    The client invests the money in an account that pays 3.25% interest only at the end of each year.

    Scheme 2
    The client invests the money in an account that pays 1.3% interest at the end of each six months.

    Investigate each scheme and recommend to Jemima, with reasons, what she should do.
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  2. #2
    Super Member

    Joined
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    Lexington, MA (USA)
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    Hello, Paulo1913!

    Jemima has $5000 to invest for two and a half years.
    Her bank offers two different investment schemes:
    . . an account that pays 3.25% interest at the end of each year,
    . . an account that pays 1.3% interest at the end of each six months.

    Investigate each scheme and recommend to Jemima, with reasons, what she should do.
    You're expected to know the compound interest formula:

    A \;=\;P\left(1 + \frac{i}{n}\right)^n

    . . where: . \begin{Bmatrix}P & = & \text{principal invested} \\ i & = & \text{periodic interest rate} \\ n & = & \text{number of periods} \\ A & = & \text{final balance} \end{Bmatrix}



    Plan A has: . \begin{array}{ccc}P & = & 5000 \\ i & = & 0.0325 \\ n & = & 2.5 \end{array}

    A \;=\;5000(1.0325)^{2.5} \;\approx\;\boxed{\$5,416.21}



    Plan B has: . \begin{array}{ccccc}P & = & 5000 \\ i & = & 0.013/2 & = 0.0065 \\ n & = & 5\end{array}

    A \;=\;5000(1.0065)^5 \;\approx\;\boxed{\$5,164.63}



    Plan A (3.25% annually) is the more profitable plan.

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