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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We use the continuous compound interest formula A = Pe^rt where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.

Then,

99,000 = 45700e^(0.124*t)

e^0.124t = 99000/45700 = 2.1663

ln(e^0.124t) = ln(2.1663)

0.124t = 0.773

t = 0.773/.124

t = 6.23 years

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