If you want an investment of $2500 to double, then you want it to get to 2500 x 2 =$5000. From the other information given in the problem, you have A = $5000, P = $2500, and r = 9% = .09. Plug those values into the formula and solve for t:

5000 = 2500 e^(.09t)

Divide by 2500

2 = e^.(09t)

Take the natural logarithm of both sides to get the variable out of the exponent.

ln 2 = ln e^(.09t)

ln 2 = (.09t) ln e

Since ln e = 1, you get...

ln 2 = .09t

Divide by .09

(ln 2)/(.09) = t

Put that expression into the calculator to get...

t = 7.7 years

May 14th, 2015

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