SOLUTION: How long does it take $100 to double it invested at 6% interest compounded continously?

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Question 600259: How long does it take $100 to double it invested at 6% interest compounded continously?
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.


200=100%2Ae%5E%280.06%2At%29 Plug in A=200, P=100, and r=0.06 (the decimal equivalent of 6%).


200%2F100=e%5E%280.06%2At%29 Divide both sides by 100.


2=e%5E%280.06%2At%29 Evaluate 200%2F100 to get 2.


ln%282%29=ln%28e%5E%280.06%2At%29%29 Take the natural log of both sides.


ln%282%29=0.06%2At%2Aln%28e%29 Pull down the exponent using the identity ln%28x%5Ey%29=y%2Aln%28x%29%29.


ln%282%29=0.06%2At%2A1 Evaluate the natural log of 'e' to get 1.


ln%282%29=0.06%2At Multiply and simplify.


0.693147180559945=0.06%2At Evaluate the natural log of 2 to get 0.693147180559945 (this value is approximate).


0.693147180559945%2F0.06=t Divide both sides by 0.06 to isolate 't'.


11.5524530093324=t Evaluate 0.693147180559945%2F0.06 to get 11.5524530093324.


t=11.5524530093324 Flip the equation.


t=12 Round to the nearest whole year.


So it will take 12 years.