How long will it take for $99,000 to grow to $45,700 at an interest rate of 12.4% if the interest compounded continuously? Round the number of years to the nearest hundredth.

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use the equation A = Pe ^{rt} for interest compounded continuously

A = Pe ^{rt}

$99,000 = $45,700 e ^{(0.124) t}

e ^{(0.124) t} = $99,000 / $45,700

e ^{(0.124) t} = 2.1663

(0.124) t = ln(2.1663)

(0.124) t = 0.773

t = 6.23 years

Hence, the answer is 6.23 years rounded to the nearest hundredth.

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