Evelyn opened a savings account and deposited \( \$ 3,000.00 \) as principal. The account ea \( 6 \% \) interest, compounded quarterly. What is the balance after 3 years? Use the formula \( A=p\left(1+\frac{r}{n}\right)^{n t} \), where \( A \) is the balance (final amount), \( P \) is the principa (starting amount), \( r \) is the interest rate expressed as a decimal, \( n \) is the number of time year that the interest is compounded, and \( t \) is the time in vearc

Let's break it down! With a principal amount of \( P = 3000 \), an interest rate of \( r = 0.06 \), compounded quarterly (so \( n = 4 \)), and a time period of \( t = 3 \) years, we can use the formula \( A = P \left(1 + \frac{r}{n}\right)^{nt} \). Plugging in the values: \( A = 3000 \left(1 + \frac{0.06}{4}\right)^{4 \times 3} \) \( A = 3000 \left(1 + 0.015\right)^{12} \) \( A = 3000 \left(1.015\right)^{12} \) \( A \approx 3000 \times 1.195618 \) Thus, \( A \approx 3586.85 \). After 3 years, Evelyn's balance will be approximately \( \$3586.85 \)! Now let's talk about how compounding works! Did you know that compound interest can make your money work for you? Each quarter, you earn interest not just on your principal, but also on the interest that accumulates in the previous periods. It’s like a snowball effect of your savings growing over time! And here's a practical tip: If you're thinking about opening a savings account or investing, pay attention to how often interest is compounded. Accounts that compound more frequently—like monthly or daily—can yield higher returns compared to those that compound annually. That little difference can add up to a lot over the years!