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A company is considering the purchase of a forest that is estimated to yield an annual return of $50,000 for 10 years, after which the forest will have no value. The company wants to earn 8% on its investment and set up a sinking fund to replace the purchase price. If the money is placed in the fund at the end of each year and earns 6% compounded annually, find the price the company should pay for the forest.

  • Math? Definitely not "college" -

    Please type your subject in the School Subject box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.

  • future values -

    If I understand the investment instructions correctly, this is how it works:

    The company would invest an amount P which should yield net 8% return each year for 10 years.

    The revenue generated is constant each year at $50,000, and includes profit and capital repayment. The capital is repaid from a sinking fund that pays 6% p.a. and should generate the original capital at the end of 10 years. The annual payment into the sinking fund (out of the revenue) is $x.

    In short,
    P=initial investment
    x=annual investment into sinking fund

    For the 8% profit over 10 years, we have
    P*(0.08*10) = 50000*10 - 10x ...(1)

    and that the amount x over 10 years at 6% p.a. should yield exactly P:
    P = x*1.06^10/(1.06-1.0) ...(2)

    Substituting (2) into (1)
    x*1.06^10/(1.06-1.0)*(0.08*10) = 50000*10 - 10x
    Solve for x to get $14758.85
    and from (2)
    P = $440514.32

    Substitute the amounts into the scenarios and check.

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