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Math Help - finace

  1. #1
    Junior Member
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    finace

    You need $10,000 in 8 years.
    i) What amount should you deposit at the end of each quarter at 6% per annum,
    compounded quarterly, so that you will have the required $10,000?
    ii) What quarterly deposit is required if the money earns 4% per annum,
    compounded quarterly?
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  2. #2
    Super Member

    Joined
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    Lexington, MA (USA)
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    Hello, Gracy!

    Is someone assigning these problems without teaching you the necessary formula?


    You need $10,000 in 8 years.
    i) What amount should you deposit at the end of each quarter at 6% per annum,
    compounded quarterly, so that you will have the required $10,000?

    This is an Annuity problem, which has this formula: . A \;= \;D\,\frac{(1 + i)^n - 1}{i}

    . . where: . \begin{array}{cccc} A &=& \text{final amount}\\ D & = &\text{periodic deposit} \\ i & = & \text{periodic interest rate} \\ n & = & \text{number of periods}\end{array}


    Solve for D:\;\;D \;= \;A\,\frac{i}{(1+i)^n - 1}

    You have: . A = 10,000,\;i = \frac{6\%}{4} = 0.015,\;n = 32

    Hence: . D \;= \; 10,000\,\frac{0.015}{1.015^{32} - 1} \;=\;245.7709697


    Therefore, you should deposit \boxed{\$245.78}* each quarter.

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    * Note that we round up.

    If we deposit \$245.77 each quarter,
    . . the final amount will be only \$9,999.96



    ii) What quarterly deposit is required if the money earns 4% per annum,
    compounded quarterly?

    Use the same formula with: . A = 10,000,\;i = \frac{4\%}{4} = 0.01,\;n = 32

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