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?

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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?

Found 3 solutions by xcentaur, ikleyn, n2:
Answer by xcentaur(357)   (Show Source):
You can put this solution on YOUR website!
e = 2.71828.
Seems familiar? Its the same as our rate.

That is our final formula.

So we get,
P=10,000
R=2.7183
Years=Y
A=20,000
Continuous compounding:

So log of 2 to the base 'e' is equal to 'Yr'
Log to the base e is also called natural logarithm,or ln()

Now to convert log to ln we need to multiply by 2.303

(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

Answer by ikleyn(53742)   (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?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        The solution in the post by the other tutor is fatally incorrect.
        I came to bring a correct solution.

The formula for the future value at continuous compounding is FV = , (1). where A is the deposited amount, 'r' is the nominal interest rate and 't' is the time in years, 'e' is the base of natural logarithms (e = 2.71828...) In your problem, A = 10,000 dollars, FV= 20,000 dollars, r = 0.1. So, formula (1) takes the form 20000 = . It implies = , 2 = . Take natural logarithm of both sides ln(2) = 0.1*t t = = 6.93147 years. ANSWEWR. The time to double the deposited amount is about 6.93 years under given conditions.

Solved correctly with complete explanations.

Answer by n2(78)   (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?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The formula for the future value at continuous compounding is FV = , (1). where A is the deposited amount, 'r' is the nominal interest rate and 't' is the time in years, 'e' is the base of natural logarithms (e = 2.71828...) In your problem, A = 10,000 dollars, FV= 20,000 dollars, r = 0.1. So, formula (1) takes the form 20000 = . It implies = , 2 = . Take natural logarithm of both sides ln(2) = 0.1*t t = = 6.93147 years. ANSWEWR. The time to double the deposited amount is about 6.93 years under given conditions.