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The terms of a single parent's will indicate that a child will receive an ordinary annuity of $20,000 per year from age 18 to age 24 (so the child can attend college) and that the balance of the estate goes to a niece. If the parent dies on the child's 17th birthday, how much money must be removed from the estate to purchase the annuity? (Assume an interest rate of 9%, compounded annually

  • math -

    Interest, i=9%=0.09 p.a.
    Future value, S

    Ordinary annuity for 6 years,
    n=6
    yearly payment, R = $20,000

    Find future value when child will be 24 years old:
    S = R((1+i)^n-1)/i
    = $20,000*(1.09^6-1)/0.09
    = $20,000*(7.523335)
    = $150,466.69

    Present value (when child is 17)
    P= S/(1+i)^7
    = $82310.43

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