Question
Tara invests $2,000 into a continuously compounding account with an annual interest rate of 5%. Use the formula P(t)=2,000e0.05t to determine how much money will be in her account after 15 years. (1 point) Responses $1,060.88 $1,060.88 $4,234.00 $4,234.00 $15,243.98 $15,243.98 $16,345.01
Answers
GPT-4o mini
To find the amount of money in Tara's account after 15 years using the formula for continuously compounding interest, we can plug \( t = 15 \) into the equation \( P(t) = 2000 e^{0.05t} \).
The formula becomes:
\[
P(15) = 2000 e^{0.05 \times 15}
\]
Calculating the exponent:
\[
0.05 \times 15 = 0.75
\]
Now, we substitute this back into the equation:
\[
P(15) = 2000 e^{0.75}
\]
Next, we need to calculate \( e^{0.75} \). Using a calculator, we find:
\[
e^{0.75} \approx 2.117
\]
Now, substituting this value into the equation gives us:
\[
P(15) = 2000 \times 2.117
\]
Calculating this product:
\[
P(15) \approx 4234
\]
Thus, the amount of money in her account after 15 years is approximately **$4,234.00**.
Therefore, the correct response is **$4,234.00**.
The formula becomes:
\[
P(15) = 2000 e^{0.05 \times 15}
\]
Calculating the exponent:
\[
0.05 \times 15 = 0.75
\]
Now, we substitute this back into the equation:
\[
P(15) = 2000 e^{0.75}
\]
Next, we need to calculate \( e^{0.75} \). Using a calculator, we find:
\[
e^{0.75} \approx 2.117
\]
Now, substituting this value into the equation gives us:
\[
P(15) = 2000 \times 2.117
\]
Calculating this product:
\[
P(15) \approx 4234
\]
Thus, the amount of money in her account after 15 years is approximately **$4,234.00**.
Therefore, the correct response is **$4,234.00**.