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.

Question

Answer:

Answer 1

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

Answer 2

u suck mathmate