Solve the problem. Round to the nearest cent as needed.
-How long will it take for $8400 to grow to $14,600 at an interest rate of 9.4% if the interest is compounded continuously? Round the number of years to the nearest hundredth.
A) 0.59 year
B) 0.06 year
C) 5.88 years
D) 58.81 years

Question

Quizplus · Accepted Answer

We can use the formula $A=P e^{rt}$ where $A$ is the final amount, $P$ is the initial amount, $r$ is the annual interest rate as a decimal, and $t$ is the number of years. Plugging in the given values, we get:

$14,600 = 8,400 e^{0.094t}$

Dividing both sides by 8,400 gives:

$1.73809524 = e^{0.094t}$

Taking the natural logarithm of both sides gives:

$0.94314718 = 0.094t$

Dividing both sides by 0.094 gives:

$t \approx 5.88$

Rounding to the nearest hundredth gives a final answer of 5.88 years. Therefore, the best choice is C.

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