Find the final amount of money in an account if
$
1
,
100
is deposited at
3
%
interest compounded semi-annually and the money is left for
6
years.

The final amount is $ . Round answer to 2 decimal places

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

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

Where:
- $ A $ is the final amount.
- $ P $ is the initial principal (1100 in this case).
- $ r $ is the annual interest rate (3% or 0.03).
- $ n $ is the number of times the interest is compounded per year (semi-annually, so $ n = 2 $).
- $ t $ is the time in years (6 years).

Let's plug the values into the formula:

\[
A = 1100 \left(1 + \frac{0.03}{2}\right)^{2 \times 6}
\]

Now, we will calculate this step by step.The final amount of money in the account after 6 years is **$1315.18**, rounded to two decimal places.

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:
1. What would the final amount be if the interest rate was 5% instead of 3%?
2. How does changing the compounding frequency affect the final amount?
3. What happens to the final amount if the deposit period increases to 10 years?
4. How does continuous compounding differ from semi-annual compounding?
5. How would the final amount change if you deposit $2000 instead of $1100?

**Tip:** Compounding more frequently results in a higher final amount due to interest being applied to accumulated interest.

Find the final amount of money in an account if $1,100 is deposited at 3% interest compounded semi-annually and the money is left for 6 years. The final amount is $ . Round answer to 2 decimal places.

Find out how to calculate the final amount in an account when $1,100 is deposited at a 3% interest rate compounded semi-annually for 6 years. Learn the steps of applying the compound interest formula and see the result rounded to two decimal places.

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