Question

Amy invests $10000 in an account that compounds annually at a rate of 11%. After 10 years, how much is in the account?
• $28.394.21
• $31,504.11
O $41.117.12
O $41,678.92

Answer 1

To calculate the future value of an investment compounded annually, you can use the formula:

\[
A = P(1 + r)^n
\]

Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested or borrowed.

For this scenario:

- \( P = 10000 \)
- \( r = 11\% = 0.11 \)
- \( n = 10 \)

Now, plug these values into the formula:

\[
A = 10000(1 + 0.11)^{10}
\]
\[
A = 10000(1.11)^{10}
\]

Calculating \( (1.11)^{10} \):

\[
(1.11)^{10} \approx 2.83942
\]

Now, multiply by 10,000:

\[
A \approx 10000 \times 2.83942 \approx 28394.21
\]

So, after 10 years, the amount in the account is approximately **$28,394.21**.

Therefore, the correct answer is:

• $28,394.21