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.