Question

Tara invests $2,000 into a continuously compounding account with an annual interest rate of 5%. Use the formula
to determine how much money will be in her account after 15 years.

A
$1,060.88

B
$4,234.00

C
$15,243.98

D
$16,345.01

Answer 1

To determine how much Tara will have in her account after 15 years with continuously compounding interest, we can use the formula for continuous compounding:

\[ A = Pe^{rt} \]

where:
- \( A \) is the amount of money accumulated after \( t \) years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( e \) is the Euler's number (approximately 2.71828).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the time in years.

Given:
- \( P = 2000 \)
- \( r = 0.05 \) (5% expressed as a decimal)
- \( t = 15 \)

Now, substitute the values into the formula:

\[ A = 2000 \cdot e^{0.05 \cdot 15} \]
\[ A = 2000 \cdot e^{0.75} \]

Next, we need to calculate \( e^{0.75} \):

Using a calculator, \( e^{0.75} \approx 2.1170 \).

Now, plug this value back into the equation:

\[ A \approx 2000 \cdot 2.1170 \]
\[ A \approx 4234.00 \]

So, after 15 years, Tara will have approximately $4,234.00 in her account.

The correct answer is:

**B $4,234.00**