SOLUTION: Suppose that ​$ 6000is invested at an interest rate of 5.8​% per​ year, compounded continuously. What is the doubling​ time?

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Question 1130374: Suppose that ​$ 6000is invested at an interest rate of 5.8​% per​ year, compounded continuously. What is the doubling​ time?
Found 3 solutions by addingup, ikleyn, MathTherapy:
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
log(2)/0.058 = 5.2 years
.
Note: The amount doesn't matter, whether it's 1 or 6000, the time will be the same for one or the other as long as the rate is the same. Rate and time determine the doubling time.
Answer by ikleyn(52769)   (Show Source): You can put this solution on YOUR website!
.
The formula for the future value of a principle compounded continuously, under given conditions is


    FV = ,


where P is the principle investment amount and  t  is the time in years.


So, the problem asks, when it will happen that


    2P = .


It impliues


    2 = 


    ln(2) = t*0.058


    t =  = 11.95 years,   or about 12 years.


Answer.  11.95 years;  12 years is enough.

Solved.

------------------

The solution by @addingup is incorrect.



Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Suppose that ​$ 6000is invested at an interest rate of 5.8​% per​ year, compounded continuously. What is the doubling​ time?
Nowhere close to what the other person says. 

Correct answer:  

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