Karen invests $2,400 into an account with a 6.8% interest that is compounded annually. How much money will she have in this account if she keeps it for 8 years?
Round your answer to the **nearest cent**.
Do **NOT** round until you have calculated the final answer.

We can calculate the amount of money Karen will have in her account using the formula for compound interest:

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

Where:
- $ A $ is the amount of money after interest.
- $ P $ is the principal (initial investment), which is $2,400.
- $ r $ is the annual interest rate, which is 6.8% or 0.068.
- $ n $ is the number of times the interest is compounded per year (since it's compounded annually, $ n = 1 $).
- $ t $ is the number of years the money is invested, which is 8.

Now, plug in the values:

\[
A = 2400 \left(1 + \frac{0.068}{1}\right)^{1 \times 8}
\]

This simplifies to:

\[
A = 2400 \left(1 + 0.068\right)^8 = 2400 (1.068)^8
\]

Now, let's compute the value.

\[
A = 2400 \times (1.068)^8
\]After 8 years, Karen will have approximately **$4,062.39** in her account.

Would you like more details on this calculation, or do you have any further questions?

Here are some related questions for further practice:
1. How would the amount change if the interest was compounded quarterly instead of annually?
2. What if the interest rate was 5% instead of 6.8%?
3. How much interest would Karen earn after 8 years?
4. If Karen invested $3,000 instead of $2,400, how much would she have after 8 years at the same rate?
5. What if Karen withdrew half of her money after 4 years, how would that affect her final balance?

**Tip:** Always remember to use the formula for compound interest carefully, ensuring you adjust for how frequently the interest is compounded.

Karen invests $2,400 into an account with a 6.8% interest that is compounded annually. How much money will she have in this account if she keeps it for 8 years? Round your answer to the nearest cent. Do NOT round until you have calculated the final answer.

Discover how to calculate the future value of $2,400 invested at 6.8% interest compounded annually over 8 years. This example walks through the compound interest formula step-by-step, helping students understand key financial math concepts. Perfect for Grades 10-12.

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