SOLUTION: How long does it take for $3800 to double if it is invested at 7% compounded continuously? Round your answer to two decimal places, if necessary.

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Question 1140176: How long does it take for $3800 to double if it is invested at 7% compounded continuously? Round your answer to two decimal places, if necessary.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
3800%2Ae%5E%280.07%2Ax%29=7600 forxyears

e%5E%280.07x%29=2
ln%28e%5E%280.07x%29%29=ln%282%29
0.07x%2Aln%28e%29=ln%282%29
0.07x=ln%282%29
x=ln%282%29%2F0.07
highlight%28x=9.902%2Ayears%29
about 9 years 47 weeks

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
How long does it take for $3800 to double if it is invested at 7% compounded continuously? Round your answer to two decimal places, if necessary.
Formula for time (t) that it takes an amount (PV) to "balloon" to a specific amount (FV), when compounded continuously: matrix%281%2C3%2C+t%2C+%22=%22%2C+ln+%28A%2FP%29%2Fr%29 

Since the investment will double the FV (A) and PV (P) are unnecessary, and so we use 2 for A, and 1 for P. 

And, with r being annual interest rate, and t being time, in years, we get: