Question

Serenity invested $16,000 in an account paying an interest rate of 4.5% compounded annually. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 9 years?

Answer 1

To calculate the amount in the account after 9 years with an initial investment of $16,000 at an interest rate of 4.5% compounded annually, we can use the formula for compound interest:

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

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.

In this case:
- \( P = 16,000 \)
- \( r = 4.5\% = 0.045 \)
- \( n = 9 \)

Now, substituting the values into the formula, we get:

\[
A = 16000(1 + 0.045)^9
\]

Calculating \( 1 + 0.045 \):

\[
1 + 0.045 = 1.045
\]

Then raise it to the power of 9:

\[
1.045^9 \approx 1.432364654
\]

Now, multiply by the principal amount:

\[
A \approx 16000 \times 1.432364654 \approx 22917.83446
\]

Rounding to the nearest hundred dollars:

\[
A \approx 22900
\]

Thus, the amount in the account after 9 years would be **$22,900**.