SOLUTION: http://www.algebra.com/tutors/students/ask.mpl How long will it take a $500 investment to be worth $700 if it is coninuously compounded at 10% per year?

Question 519354: http://www.algebra.com/tutors/students/ask.mpl
How long will it take a $500 investment to be worth $700 if it is coninuously compounded at 10% per year?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the continuous compounding formula.

Plug in , , and (the decimal equivalent of 10%).

Divide both sides by .

Evaluate to get .

Take the natural log of both sides.

Pull down the exponent using the identity .

Evaluate the natural log of 'e' to get 1.

Multiply and simplify.

Evaluate the natural log of to get (this value is approximate).

Divide both sides by to isolate 't'.

Evaluate to get .

Flip the equation.

So it will take roughly 3.36 years.
RELATED QUESTIONS
MathLover1 has a reputation to provide incorrect solutions. Here is one she posted... (answered by ikleyn)

How do you write 17! as the difference of two integer perfect squares? Ms.Ikelyn... (answered by ikleyn,math_tutor2020)

How long will it take a $700 investment to be worth $800 if it is continuously compounded (answered by Fombitz)

Ms.Ikelyn, I asked a question here:... (answered by MathLover1)

Ms.Ikelyn, for the solution you gave for the problem here:... (answered by math_tutor2020)

Dear MathTutor, I appreciate your response on the question I asked regarding the... (answered by math_tutor2020)

I posted a problem here:... (answered by greenestamps)

Hi, This solution makes no sense. Please help!... (answered by mananth)

Hi, I need help on the question from this, and have a question for Ms.Ikelyn:... (answered by MathLover1,ikleyn)