Brenda invests $4,848 in a savings account with a fixed annual interest rate of 5% compounded yearly. What will the account balance be after 6 years?

To calculate the account balance after 6 years, we use the formula for compound interest:

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

Where:
- $A$ is the future value (the account balance after 6 years),
- $P$ is the principal amount (the initial investment, $4,848),
- $r$ is the annual interest rate (5% or 0.05),
- $n$ is the number of times the interest is compounded per year (since it is compounded yearly, $n = 1$),
- $t$ is the time in years (6 years).

Now plug in the values:

\[
A = 4848 \left(1 + \frac{0.05}{1}\right)^{1 \times 6}
\]
\[
A = 4848 \left(1.05\right)^6
\]

Let's calculate this value.The account balance after 6 years will be approximately $6,496.78.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How does changing the interest rate affect the final amount?
2. What would the balance be if the interest were compounded monthly instead of yearly?
3. How much total interest did Brenda earn in 6 years?
4. What is the formula for continuous compounding, and how does it compare with yearly compounding?
5. What would the future value be after 10 years instead of 6?

**Tip:** Increasing the compounding frequency results in a higher final amount due to the effect of interest on interest.

Learn how to calculate compound interest after 6 years on an investment of $4,848 at an annual interest rate of 5%. This problem involves using the compound interest formula to determine the future value of Brenda's savings account. Suitable for high school students studying finance and compound interest calculations.

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