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?

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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) About Me  (Show Source):
You can put this solution on YOUR website!

A=Pe%5E%28rt%29 Start with the continuous compounding formula.


700=500%2Ae%5E%280.1%2At%29 Plug in A=700, P=500, and r=0.1 (the decimal equivalent of 10%).


700%2F500=e%5E%280.1%2At%29 Divide both sides by 500.


1.4=e%5E%280.1%2At%29 Evaluate 700%2F500 to get 1.4.


ln%281.4%29=ln%28e%5E%280.1%2At%29%29 Take the natural log of both sides.


ln%281.4%29=0.1%2At%2Aln%28e%29 Pull down the exponent using the identity ln%28x%5Ey%29=y%2Aln%28x%29%29.


ln%281.4%29=0.1%2At%2A1 Evaluate the natural log of 'e' to get 1.


ln%281.4%29=0.1%2At Multiply and simplify.


0.336472236621213=0.1%2At Evaluate the natural log of 1.4 to get 0.336472236621213 (this value is approximate).


0.336472236621213%2F0.1=t Divide both sides by 0.1 to isolate 't'.


3.36472236621213=t Evaluate 0.336472236621213%2F0.1 to get 3.36472236621213.


t=3.36472236621213 Flip the equation.




So it will take roughly 3.36 years.