Find the final amount of money in an account if  
$
1
,
100
  is deposited at  
2.5
%
  interest compounded semi-annually and the money is left for  
9
  years.

The final amount is $ 
. Round to the nearest cent.

To find the final amount of money in the account, we can use the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the final amount of money in the account.
- $ P = 1,100 $ is the initial deposit (principal).
- $ r = 0.025 $ is the annual interest rate (2.5%).
- $ n = 2 $ is the number of times the interest is compounded per year (semi-annually).
- $ t = 9 $ is the number of years the money is left in the account.

Now, let's plug in the values and calculate the final amount.

\[
A = 1,100 \left(1 + \frac{0.025}{2}\right)^{2 \times 9}
\]

\[
A = 1,100 \left(1 + 0.0125\right)^{18}
\]

\[
A = 1,100 \left(1.0125\right)^{18}
\]

Now I will compute this step.The final amount of money in the account after 9 years, with $ 1,100 $ deposited at 2.5% interest compounded semi-annually, is approximately **\$1,375.64**.

Would you like further details on the calculation or clarification on any part of the process?

Here are 5 related questions to expand on this:
1. How would the result change if the interest was compounded quarterly instead of semi-annually?
2. What if the interest rate was 3% instead of 2.5%?
3. How does the length of time affect the growth of compound interest?
4. How can you calculate the interest earned separately from the final amount?
5. What happens if no interest is compounded (i.e., simple interest is applied)?

**Tip:** The more frequently interest is compounded, the greater the final amount, since interest is earned on previously accumulated interest.

Find the final amount of money in an account if $1,100 is deposited at 2.5% interest compounded semi-annually and the money is left for 9 years. The final amount is $____. Round to the nearest cent.

Learn how to calculate the final amount of money in an account when $1,100 is deposited at 2.5% interest compounded semi-annually for 9 years. This problem applies the compound interest formula and covers exponential growth in financial mathematics. Suitable for Grades 9-12.

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