How long will it take $500 to triple if it is invested at 9% annual interest, compounded continuously?
A) It will take approximately 11.1 years.
B) It will take approximately 12.9 years.
C) It will take approximately 12.2 years.
D) It will take approximately 5.3 years.
E) It will take approximately 11.9 years.

Question

Quizplus · Accepted Answer

We can use the formula for continuous compounding:

A = Pe^(rt)

where A is the final amount, P is the initial amount, e is Euler's number (approximately 2.71828), r is the interest rate, and t is time in years.

We want to triple the initial amount, so A = 3P. We know P = $500 and r = 9%. Plugging in these values, we get:

3P = Pe^(0.09t)

Dividing both sides by P:

3 = e^(0.09t)

Taking the natural logarithm of both sides:

ln(3) = 0.09t

Solving for t:

t = ln(3)/0.09 ≈ 12.2 years

Therefore, it will take approximately 12.2 years for $500 to triple at 9% annual interest, compounded continuously.

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