Question

How long will it take for $1000 to grow to $5000 at an interest rate of 3.5% compounded continuously?

a) Approximately 10.14 years
b) Approximately 8.36 years
c) Approximately 12.32 years
d) Approximately 15.45 years

Answer 1

To find out how long it will take for $1000 to grow to $5000 at an interest rate of 3.5% compounded continuously, use the formula for continuous compound interest and solve for time. The answer is approximately 8.36 years.

Step-by-step explanation:

To find out how long it will take for $1000 to grow to $5000 at an interest rate of 3.5% compounded continuously, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:

• A is the final amount ($5000)
• P is the initial amount ($1000)
• r is the interest rate (0.035)
• t is the time in years (which we want to find)

Plugging in the values:

5000 = 1000 * e^(0.035t)

Simplifying the equation:

e^(0.035t) = 5

Taking the natural logarithm (ln) of both sides:

0.035t ln(e) = ln(5)

ln(e) is equal to 1:

0.035t = ln(5)

Dividing both sides by 0.035:

t = ln(5) / 0.035

Using a calculator to evaluate the expression:

t ≈ 8.36 years

Therefore, the answer is approximately 8.36 years. So the correct option is b) Approximately 8.36 years.