Question

How long will it take for $1300 to grow to $45,600 at an interest rate of 8.9% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

A) 3.22 years
B) 4.76 years
C) 4.09 years
D) 3.94 years

Answer 1

To find the time it takes for $1300 to grow to $45,600 at an interest rate of 8.9% compounded continuously, we can use the continuous compound interest formula. Plugging in the values and solving for t gives us approximately 4.09 years.

Step-by-step explanation:

To solve this problem, we can use the continuous compound interest formula:

A = P*e^(rt)

Where:

• A is the future value ($45,600)
• P is the initial amount ($1300)
• r is the interest rate (8.9% or 0.089)
• t is the time in years (unknown)

Plugging in the values, we get:

45,600 = 1300*e^(0.089t)

Divide both sides by 1300 to isolate the exponential term:

35.077 = e^(0.089t)

Take the natural logarithm (ln) of both sides to eliminate the exponential:

ln(35.077) = 0.089t

Divide both sides by 0.089 to solve for t:

t = ln(35.077) / 0.089

Using a calculator, we find that t is approximately 4.09 years.