SOLUTION: A commonly asked question is, "How long will it take to double my money?" At 10% interest rate and continuous compounding, what is the answer? Round to the hundredth's place. PLEA

Question 73569: A commonly asked question is, "How long will it take to double my money?" At 10% interest rate and continuous compounding, what is the answer? Round to the hundredth's place. PLEASE HELP!!! I Would Appreciate it!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A commonly asked question is, "How long will it take to double my money?" At 10% interest rate and continuous compounding, what is the answer? Round to the hundredth's place.
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Continuous compounding gives A = Pe^rt
P is the initial investment; if you double it you get 2P
2P = Pe^rt
Divide both sides by P to get:
2 = e^rt
Take the natural log of boh sides to get:
ln2 = rt
t= (1/r)ln2
If r=10% you get:
t = (1/0.1)(0.69314...)

t= 6.9314 years to double your money at 10% annual interest.
This is usually called "the rule of 7".
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Cheers,
Stan H.
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