Lea invests $8,333 in a savings account with a fixed annual interest rate of 8% compounded yearly. What will the account balance be after 12 years?

To calculate the account balance after 12 years with an annual interest rate compounded yearly, we can use the formula for compound interest:

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

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 (in decimal form).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested for, in years.

Given:
- $ P = 8,333 $ dollars
- $ r = 8\% = 0.08 $
- $ n = 1 $ (since it's compounded yearly)
- $ t = 12 $ years

Substitute these values into the formula:

\[
A = 8333 \left(1 + \frac{0.08}{1}\right)^{1 \times 12}
\]

\[
A = 8333 \times (1.08)^{12}
\]

Now, let's calculate the value of $ A $.

\[
A \approx 8333 \times 2.51817 \approx 20985.74
\]

So, the account balance after 12 years will be approximately **$20,985.74**.

Would you like more details or have any questions?

Here are some related questions:
1. What would the balance be if the interest rate was compounded quarterly?
2. How much interest will be earned after 12 years?
3. What if Lea decides to withdraw half of the money after 6 years and reinvests the remaining amount?
4. How does the compound interest formula change if interest is compounded monthly?
5. How long would it take for Lea's investment to double at the same interest rate?

**Tip:** When solving for compound interest, remember to adjust the number of compounding periods per year in the formula if interest is compounded more frequently than annually.

Discover how to calculate the account balance after 12 years with an annual interest rate of 8% compounded yearly. Use our step-by-step guide and compound interest formula to find out the final balance. Suitable for students and anyone interested in financial calculations.

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