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Find the time it takes for $6,400 to double when invested at an annual interest rate of 7%, compounded continuously.

User Copumpkin
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Final answer:

To find the time it takes for $6,400 to double when invested at an annual interest rate of 7%, compounded continuously, use the formula A = P * e^(rt). Plugging in the values, we find that t ≈ 9.90 years.

Step-by-step explanation:

To find the time it takes for $6,400 to double when invested at an annual interest rate of 7%, compounded continuously, we can use the formula:

A = P * e^(rt)

Where:

  • A is the final amount
  • P is the initial amount
  • e is the base of the natural logarithm
  • r is the interest rate
  • t is the time in years

In this case, we want the final amount to be twice the initial amount, so A = 2P. Plugging in the values, we have:

2P = P * e^(0.07t)

Dividing both sides by P, we get:

2 = e^(0.07t)

Taking the natural logarithm of both sides, we have:

ln(2) = 0.07t

Dividing both sides by 0.07, we get:

t = ln(2) / 0.07

Using a calculator, we find that t ≈ 9.90 years.

User Duc Nguyen
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