SOLUTION: Suppose that $2000 is invested in an account that pays interest compounded continuously. Find the amount of time that it would take for the account to grow to $4000 at 3.75 %.

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Question 1057999: Suppose that $2000 is invested in an account that pays interest compounded continuously. Find the amount of time that it would take for the account to grow to $4000 at 3.75 %.
Answer by solve_for_x(190) About Me  (Show Source):
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Use the equation for continuous compounding:

A+=+Pe%5E%28rt%29

with A = 4000, P = 2000, and r = 0.0375.

Substituting the value for A, P, and r into the equation and
solving for t gives:

4000+=+2000%2Ae%5E%280.0375t%29

2+=+e%5E%280.0375t%29

ln(2) = 0.0375t

t = ln(2) / 0.0375

t = 18.48 years