$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.