Suppose that the machinery in question costs $118000 and earns profit at a continuous rate of $61000 per year. Use an interest rate of 7.25% 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

Suppose that the machinery in question costs $118000 and earns profit at a continuous rate of $61000 per year.  Use an interest rate of 7.25% 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.

amistre64 · Answer

Is the equation to use:

118 = 61e^(.0725t) ??

amistre64 · Answer

ln(118/61) = .0725t

ln(118/61)
--------- = t  i guess
  .0725

mathteacher1729 · Answer

This is why you* never see interest rates like 7.25%.  

 ln(118/61)/0.725 ~~ 0.91 years.  (meaning you would make back your cost before year's end)

* you = "NOT the bank or credit card company" ;-p

mathteacher1729 · Answer

Also, this is a pretty nice page page with well written examples: http://www.mathwarehouse.com/compound-interest/continuously-compounded-interest.php