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Math Help - semi-annual compounding question

  1. #1
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    semi-annual compounding question

    Parents want to invest a sum of money at the birth of a child so that when the child becomes 18 years of age, the child will receive $20,000 per year toward college expenses in four yearly installments. If the nominal rate of return per year is 6%, and interest is compounded semi-annually, how much should the original investment be?
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  2. #2
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    First, find the effective annual rate of return.

    1+i = \left( 1+\frac{0.06}{2} \right)^2
    i=6.09\%

    Now, find the value of 4 payments of 20000, paid in advance
    v=\frac{1}{1+i}

    d=iv

    PV = 20000 \times \frac{1-v^4}{d}

    PV = 20000 \times 3.66857

    PV = 73371.34

    Now, these payments start on the 18th birthday. their value at birth is

    PV' = 73371.34 \times v^{18}
    PV' = 25315.49
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