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# You have \$100 invested into an account that earns 5% interest compounded continuously....

kristenmarieb... | Student, Grade 10 | Valedictorian

Posted August 22, 2013 at 5:56 PM via web

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You have \$100 invested into an account that earns 5% interest compounded continuously.  The future value of the account will be A = 100e^(.05t) in t years.

How long will it take for your \$100 to double?

(Let A = 200) Solve for t

Round to one decimal.

Tagged with algebra 2, math

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 22, 2013 at 6:02 PM (Answer #1)

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The value of \$100 invested in the account after t years is given by A = 100*e^(0.05*t).

Let T be the time taken for the amount to become double.

200 = 100*e^(0.05*T)

=> 2 = e^(0.05*T)

Take the natural logarithm of both the sides

ln 2 = ln(e^(0.05*T))

Use the property log a^b = b*log a and log_a a = 1

=> ln 2 = 0.05*T*1

=> T = (ln 2)/0.05

=> T `~~` 13.9

The amount in the account becomes double in 13.9 years.

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