SOLUTION: A commonly asked question is, "How long will it take to double my money?" At 10% interest rate and continous compounding, what is the answer? The base amount should be $10,000 and

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Question 33003: A commonly asked question is, "How long will it take to double my money?" At 10% interest rate and continous compounding, what is the answer?
The base amount should be $10,000 and the compounding rate is 2.7183.
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
e = 2.71828.
Seems familiar? Its the same as our rate.
+A++=+++P%28e%29%5EYr
That is our final formula.


So we get,
P=10,000
R=2.7183
Years=Y
A=20,000
Continuous compounding:
+A++=+++P%28e%29%5EYr
+20000=10000%28e%29%5EYr
+2+=+%28e%29%5EYr
So log of 2 to the base 'e' is equal to 'Yr'
Log to the base e is also called natural logarithm,or ln()
+Ln%282%29+=+Yr+
+Ln%282%29+=+Y%282.7183%29+
+%28Ln%282%29%29%2F2.7183+=+Y+
Now to convert log to ln we need to multiply by 2.303
+Y+=+%28Ln%282%29%29%2F2.7183+
+Y+=+2.303%2ALog%282%29%2F2.7183+
+Y+=+0.8472%2ALog%282%29+
+Y+=+0.8472%2A0.3010+ (from log tables)
Y=0.255
Obviously,this is a bit small,so adjusting the decimal values we get:
Y=25.5


So to double your money at continous compound rate 'e',
you'd need 25.5 years.


Hope this helps,
xC