SOLUTION: How long, to the nearest year, will it take me to become a millionaire if I invest $1000 at 9% interest compounded continuously?

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Question 506930: How long, to the nearest year, will it take me to become a millionaire if I invest $1000 at 9% interest compounded continuously?
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.


1000000=1000%2Ae%5E%280.09%2At%29 Plug in A=1000000, P=1000, and r=0.09 (the decimal equivalent of 9%).


1000000%2F1000=e%5E%280.09%2At%29 Divide both sides by 1000.


1000=e%5E%280.09%2At%29 Evaluate 1000000%2F1000 to get 1000.


ln%281000%29=ln%28e%5E%280.09%2At%29%29 Take the natural log of both sides.


ln%281000%29=0.09%2At%2Aln%28e%29 Pull down the exponent using the identity ln%28x%5Ey%29=y%2Aln%28x%29%29.


ln%281000%29=0.09%2At%2A1 Evaluate the natural log of 'e' to get 1.


ln%281000%29=0.09%2At Multiply and simplify.


6.90775527898214=0.09%2At Evaluate the natural log of 1000 to get 6.90775527898214 (this value is approximate).


6.90775527898214%2F0.09=t Divide both sides by 0.09 to isolate 't'.


76.7528364331349=t Evaluate 6.90775527898214%2F0.09 to get 76.7528364331349.


t=76.7528364331349 Flip the equation.


t=77 Round to the nearest whole year.


So it will take roughly 77 years.

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
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Thanks,

Jim