SOLUTION: An amount of money was invested in an account which earned interest at a rate compounded continuously. After 11 years, the investment doubled. Determine the interest rate used at t

Question 539448: An amount of money was invested in an account which earned interest at a rate compounded continuously. After 11 years, the investment doubled. Determine the interest rate used at the time of investment.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
An amount of money was invested in an account which earned interest at a rate compounded continuously. After 11 years, the investment doubled. Determine the interest rate used at the time of investment.
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Formula: A(t) = Ao*e^(rt)
Ao is the amount invested.
A(t) is the value after t years.
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When A(t) = 2*Ao the investment has doubled.
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Solve: e^(rt) = 2 for "r" when t = 11.
e^(11r) = 2
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Take the natural log:
11r = ln(2)
r = 0.0630
rate = 6.3%
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Cheers,
Stan H.
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