SOLUTION: How many years will it take for a $100 investment to grow to $700 if it is compounded continuously at a rate of 9%? A(t)= P*e^rt

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Question 703336: How many years will it take for a $100 investment to grow to $700 if it is compounded continuously at a rate of 9%?
A(t)= P*e^rt
Found 2 solutions by jim_thompson5910, solver91311:
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 9%).


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.


Round to the nearest whole year.

So it will take about 22 years.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


If 100 grows to 700, then A divided by P is 7.



Solve for

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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