# 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.

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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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