$2500 is invested in an account that pays 12% interest, compounded continuously. Find the time required for the amount to triple. Round your answer to the nearest tenth of a year.

e^.12t = 3

To find the time required for the amount to triple, we need to use the continuous compound interest formula:

A = P * e^(rt)

Where:
A = Final amount (triple the initial amount)
P = Initial investment ($2500)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (12% or 0.12)
t = Time in years (what we're trying to find)

We can rewrite the formula as:

3P = P * e^(0.12t)

Divide both sides of the equation by P:

3 = e^(0.12t)

To solve for t, we take the natural logarithm of both sides:

ln(3) = 0.12t

Now, divide both sides by 0.12:

t = ln(3) / 0.12

Using a calculator, we find:

t ≈ 6.01 years

Therefore, it would take approximately 6.01 years for the amount to triple. Rounded to the nearest tenth of a year, the answer is 6.0 years.