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Find the time it takes for $8,800 to double when invested at an annual interest rate of 6%, compounded continuously?

User Jsantell
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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.

User Chris Woods
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