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

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) (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 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
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim
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