Question

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:

Answers

MathMate
Continuous compounding:
future value = present value * e<sup>rt</sup>
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 * e<sup>rt</sup>
e<sup>rt</sup> = 104000/69000
r=0.09
Solve for t.
hint: take log to the base e and solve.
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