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.
P(t)= 2000e^0.05t

A
$1,060.88

B
$4,234.00

C
$15,243.98

D
$16,345.01

Answer 1

To find out how much money will be in Tara's account after 15 years using the formula for continuously compounded interest, we can use the given formula:

\[
P(t) = 2000e^{0.05t}
\]

where:
- \( P(t) \) is the amount of money in the account after \( t \) years,
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828),
- \( 0.05 \) is the annual interest rate as a decimal,
- \( t \) is the number of years.

In this case, we substitute \( t = 15 \):

\[
P(15) = 2000e^{0.05 \times 15}
\]

Calculating \( 0.05 \times 15 \):

\[
0.05 \times 15 = 0.75
\]

Now we substitute back into the equation:

\[
P(15) = 2000e^{0.75}
\]

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

Using a calculator:

\[
e^{0.75} \approx 2.117
\]

Finally, we multiply this by 2000:

\[
P(15) \approx 2000 \times 2.117 \approx 4234
\]

Thus,

\[
P(15) \approx 4234.00
\]

Therefore, the amount in Tara's account after 15 years will be approximately **$4,234.00**.

The correct answer is **B $4,234.00**.