Isabella invests $10,000 in an account that is compounded continuously at an annual interest rate of 3%, according to the formula A=Pert , where A is the amount accrued, P is the principal, r is the rate of interest, and t is the time, in years. Apply the formula to find out how much Isabella’s investment will be worth in 15 years, to the nearest dollar.(1 point)

Question

Responses

$15,683
$15,683

$13,499
$13,499

$900,171
$900,171

$10,304

Answer 1

To find out how much Isabella's investment will be worth in 15 years using the formula for continuous compounding, we can substitute the values into the formula \( A = Pe^{rt} \).

Here are the specifics:

• \( P = 10,000 \) (the principal)
• \( r = 0.03 \) (the annual interest rate in decimal form)
• \( t = 15 \) (the time in years)
• \( e \) is the base of the natural logarithm, approximately equal to 2.71828

Now we can calculate \( A \):

\[ A = 10,000 \cdot e^{(0.03 \cdot 15)} \]

First, calculate \( 0.03 \cdot 15 \):

\[ 0.03 \cdot 15 = 0.45 \]

Now find \( e^{0.45} \):

Using a calculator, \( e^{0.45} \approx 1.56831 \).

Now we can calculate \( A \):

\[ A \approx 10,000 \cdot 1.56831 \approx 15,683.10 \]

Rounding to the nearest dollar, Isabella’s investment will be worth approximately:

\[ A \approx 15,683 \]

Therefore, the correct answer is:

$15,683