SOLUTION: How long would it take to double your principal at an annual interest rate of 8% compounded continuously?
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Question 308449: How long would it take to double your principal at an annual interest rate of 8% compounded continuously?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I'll do you one better. Rather than answering that exact question, I'll give you a formula calculating the time to make any desired multiplication of your principal at any annual interest rate.
The formula for Future Value, 
, of an investment, 
, at an annual interest rate of 
, for a period of 
years is:
Where 
is the base of the natural logarithms.
For your specific problem, we want to be equal to 
, which means that we want to determine the value of that makes 
when 
.
So, in general, for a given multiplier, 
, we want 
. (
in your problem)
That means that we want:
Take the natural log of both sides:
\ =\ \ln(m))
Apply the rule for raising a the argument of a logarithm to a power:
\ =\ \ln(m))
Recall that \ =\ 1)
)
And then divide by
}{r})
For this specific problem, plug in 0.08 for and 2 for . Then punch the buttons on your calculator.
John
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