Calculus

Suppose that the machinery in question costs $104000 and earns profit at a continuous rate of $69000 per year. Use an interest rate of 9% per year, compounded continuously. When is the present value of the profit equal to the cost of the machinery? Round your answer to the nearest tenth of a year.

Answer:

  1. 👍 0
  2. 👎 0
  3. 👁 587
asked by Erika
  1. Continuous compounding:
    future value = present value * ert
    where t=number of periods, and r=rate

    So assuming the cost of the machinery remains constant, then equate future value of the profit to the cost:
    104000 = 69000 * ert
    ert = 104000/69000
    r=0.09
    Solve for t.
    hint: take log to the base e and solve.

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    posted by MathMate

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