Final answer:
To find the time it takes for $8,800 to double when invested at an annual interest rate of 6%, we can use the formula for continuous compound interest. Plugging in the values and solving, the time comes out to be approximately 11.55 years.
Step-by-step explanation:
To find the time it takes for $8,800 to double when invested at an annual interest rate of 6% compounded continuously, you can use the formula for continuous compound interest:
A = P * e^(rt)
where:
A is the final amount (in this case, double the initial amount)
P is the principal amount (in this case, $8,800)
e is the base of the natural logarithm (approximately 2.71828)
r is the annual interest rate (in this case, 6% or 0.06)
t is the time in years (what we're trying to find)
Plugging in the values, we have:
A = 2P = 2 * $8,800 = $17,600
Now we can solve for t:
$17,600 = $8,800 * e^(0.06t)
Dividing both sides by $8,800, we get:
2 = e^(0.06t)
To isolate t, take the natural logarithm of both sides:
ln(2) = 0.06t
Divide both sides by 0.06:
t = ln(2) / 0.06
Using a calculator, we find that t ≈ 11.55 years.